title: Virtual reality

text: Since 2017, major strides in the integration of Virtual Reality and Cognitive Behavioral Therapy have been made, focusing on how to tailor the experience to suit each individual patient.


title: Virtual reality

text: With the COVID-19 restrictions in 2020, VR is experiencing an enormous rise. According to Grand View Research, the global VR market will grow to 62.1 billion dollars in 2027.


title: Virtual reality

text: Now in the post-pandemic era, augmented reality and virtual technologies have created a new avenue that may influence the future of occupational safety training and rehabilitation.


title: Virtual reality

text: The Virtual Reality Modelling Language (VRML), first introduced in 1994, was intended for the development of "virtual worlds" without dependency on headsets. The Web3D consortium was subsequently founded in 1997 for the development of industry standards for web-based 3D graphics. The consortium subsequently developed X3D from the VRML framework as an archival, open-source standard for web-based distribution of VR content. WebVR is an experimental JavaScript application programming interface (API) that provides support for various virtual reality devices, such as the HTC Vive, Oculus Rift, Google Cardboard or OSVR, in a web browser.


title: Virtual reality

text: Modern virtual reality headset displays are based on technology developed for smartphones including: gyroscopes and motion sensors for tracking head, body, and hand positions; small HD screens for stereoscopic displays; and small, lightweight and fast computer processors. These components led to relative affordability for independent VR developers, and led to the 2012 Oculus Rift Kickstarter offering the first independently developed VR headset.


title: Virtual reality

text: Independent production of VR images and video has increased alongside the development of affordable omnidirectional cameras, also known as 360-degree cameras or VR cameras, that have the ability to record 360 interactive photography, although at relatively low resolutions or in highly compressed formats for online streaming of 360 video. In contrast, photogrammetry is increasingly used to combine several high-resolution photographs for the creation of detailed 3D objects and environments in VR applications.


title: Virtual reality

text: To create a feeling of immersion, special output devices are needed to display virtual worlds. Well-known formats include head-mounted displays or the CAVE. In order to convey a spatial impression, two images are generated and displayed from different perspectives (stereo projection). There are different technologies available to bring the respective image to the right eye. A distinction is made between active (e.g. shutter glasses) and passive technologies (e.g. polarizing filters or Infitec).


title: Virtual reality

text: In order to improve the feeling of immersion, wearable multi-string cables offer haptics to complex geometries in virtual reality. These strings offer fine control of each finger joint to simulate the haptics involved in touching these virtual geometries.


title: Virtual reality

text: Special input devices are required for interaction with the virtual world. Some of the most common input devices are motion controllers and optical tracking sensors. In some cases, wired gloves are used. Controllers typically use optical tracking systems (primarily infrared cameras) for location and navigation, so that the user can move freely without wiring. Some input devices provide the user with force feedback to the hands or other parts of the body, so that the human being can orientate himself in the three-dimensional world through haptics and sensor technology as a further sensory sensation and carry out realistic simulations. This allows for the viewer to have a sense of direction in the artificial landscape. Additional haptic feedback can be obtained from omnidirectional treadmills (with which walking in virtual space is controlled by real walking movements) and vibration gloves and suits.


title: Virtual reality

text: Virtual reality cameras can be used to create VR photography using 360-degree panorama videos. 360-degree camera shots can be mixed with virtual elements to merge reality and fiction through special effects. VR cameras are available in various formats, with varying numbers of lenses installed in the camera.


title: Virtual reality

text: Minimal Angle of Resolution (MAR) refers to the minimum distance between two display pixels. At the distance, viewer can clearly distinguish the independent pixels. Often measured in arc-seconds, MAR between two pixels has to do with the viewing distance. For the general public, resolution is about 30-65 arc-seconds, which is referred to as the spatial resolution when combined with distance. Given the viewing distance of 1m and 2m respectively, regular viewers won't be able to perceive two pixels as separate if they are less than 0.29mm apart at 1m and less than 0.58mm apart at 2m.


title: Virtual reality

text: Most small-size displays have a refresh rate of 60 Hz, which adds about 15ms of additional latency. The number is reduced to less than 7ms if the refresh rate is increased to 120 Hz or even 240 Hz and more. Participants generally feel that the experience is more immersive with higher refresh rates as a result. However, higher refresh rates require a more powerful graphics processing unit.


title: Virtual reality

text: In assessing the achieved immersion by a VR device, we need to consider our field of view (FOV) in addition to quality image. Our eyes have a horizontal FOV of about 140 degrees per side and a vertical FOV of roughly 175 degrees. Binocular vision is limited to 120 degrees horizontally where the right and the left visual fields overlap. Overall, we have a FOV of roughly 300 degrees x 175 degrees with two eyes, i.e., approximately one third of the full 360-deg sphere.


title: Virtual reality

text: Virtual reality is most commonly used in entertainment applications such as video games, 3D cinema, amusement park rides including dark rides and social virtual worlds. Consumer virtual reality headsets were first released by video game companies in the early-mid 1990s. Beginning in the 2010s, next-generation commercial tethered headsets were released by Oculus (Rift), HTC (Vive) and Sony (PlayStation VR), setting off a new wave of application development. 3D cinema has been used for sporting events, pornography, fine art, music videos and short films. Since 2015, roller coasters and theme parks have incorporated virtual reality to match visual effects with haptic feedback. VR not only fits the trend of the digital industry but also enhances the film's visual effect. The film gives the audience more ways to interact through VR technology.


title: Virtual reality

text: In social sciences and psychology, virtual reality offers a cost-effective tool to study and replicate interactions in a controlled environment. It can be used as a form of therapeutic intervention. For instance, there is the case of the virtual reality exposure therapy (VRET), a form of exposure therapy for treating anxiety disorders such as post traumatic stress disorder (PTSD) and phobias.


title: Virtual reality

text: Virtual reality programs are being used in the rehabilitation processes with elderly individuals that have been diagnosed with Alzheimer's disease. This gives these elderly patients the opportunity to simulate real experiences that they would not otherwise be able to experience due to their current state. 17 recent studies with randomized controlled trials have shown that virtual reality applications are effective in treating cognitive deficits with neurological diagnoses. Loss of mobility in elderly patients can lead to a sense of loneliness and depression. Virtual reality is able to assist in making aging in place a lifeline to an outside world that they cannot easily navigate. Virtual reality allows exposure therapy to take place in a safe environment.


title: Virtual reality

text: In medicine, simulated VR surgical environments were first developed in the 1990s. Under the supervision of experts, VR can provide effective and repeatable training at a low cost, allowing trainees to recognize and amend errors as they occur.


title: Virtual reality

text: Virtual reality has been used in physical rehabilitation since the 2000s. Despite numerous studies conducted, good quality evidence of its efficacy compared to other rehabilitation methods without sophisticated and expensive equipment is lacking for the treatment of Parkinson's disease. A 2018 review on the effectiveness of mirror therapy by virtual reality and robotics for any type of pathology concluded in a similar way. Another study was conducted that showed the potential for VR to promote mimicry and revealed the difference between neurotypical and autism spectrum disorder individuals in their response to a two-dimensional avatar.


title: Virtual reality

text: Immersive virtual reality technology with myoelectric and motion tracking control may represent a possible therapy option for treatment-resistant phantom limb pain. Pain scale measurements were taken into account and an interactive 3-D kitchen environment was developed bases on the principles of mirror therapy to allow for control of virtual hands while wearing a motion-tracked VR headset. A systematic search in Pubmed and Embase was performed to determine results that were pooled in two meta-analysis. Meta-analysis showed a significant result in favor of VRT for balance.


title: Virtual reality

text: In the fast-paced and globalised business world meetings in VR are used to create an environment in which interactions with other people (e.g. colleagues, customers, partners) can feel more natural than a phone call or video chat. In the customisable meeting rooms all parties can join using the VR headset and interact as if they are in the same physical room. Presentations, videos or 3D models (of e.g. products or prototypes) can be uploaded and interacted with. Compared to traditional text-based CMC, Avatar-based interactions in 3D virtual environment lead to higher levels of consensus, satisfaction, and cohesion among group members.


title: Virtual reality

text: VR can simulate real workspaces for workplace occupational safety and health purposes, educational purposes, and training purposes. It can be used to provide learners with a virtual environment where they can develop their skills without the real-world consequences of failing. It has been used and studied in primary education, anatomy teaching, military, astronaut training, flight simulators, miner training, medical education, geography education, architectural design, driver training and bridge inspection. Immersive VR engineering systems enable engineers to see virtual prototypes prior to the availability of any physical prototypes. Supplementing training with virtual training environments has been claimed to offer avenues of realism in military and healthcare training while minimizing cost. It also has been claimed to reduce military training costs by minimizing the amounts of ammunition expended during training periods. VR can also be used for the healthcare training and education for medical practitioners.


title: Virtual reality

text: In the engineering field, VR has proved very useful for both engineering educators and the students. A previously expensive cost in the educational department now being much more accessible due to lowered overall costs, has proven to be a very useful tool in educating future engineers. The most significant element lies in the ability for the students to be able to interact with 3-D models that accurately respond based on real world possibilities. This added tool of education provides many the immersion needed to grasp complex topics and be able to apply them. As noted, the future architects and engineers benefit greatly by being able to form understandings between spatial relationships and providing solutions based on real-world future applications.


title: Virtual reality

text: The first fine art virtual world was created in the 1970s. As the technology developed, more artistic programs were produced throughout the 1990s, including feature films. When commercially available technology became more widespread, VR festivals began to emerge in the mid-2010s. The first uses of VR in museum settings began in the 1990s, seeing a significant increase in the mid-2010s. Additionally, museums have begun making some of their content virtual reality accessible.


title: Virtual reality

text: Virtual reality's growing market presents an opportunity and an alternative channel for digital marketing. It is also seen as a new platform for e-commerce, particularly in the bid to challenge traditional "brick and mortar" retailers. However, a 2018 study revealed that the majority of goods are still purchased in physical stores.


title: Virtual reality

text: In the case of education, the uses of virtual reality have demonstrated being capable of promoting higher order thinking, promoting the interest and commitment of students, the acquisition of knowledge, promoting mental habits and understanding that are generally useful within an academic context.


title: Virtual reality

text: A case has also been made for including virtual reality technology in the context of public libraries. This would give library users access to cutting-edge technology and unique educational experiences. This could include giving users access to virtual, interactive copies of rare texts and artifacts and to tours of famous landmarks and archeological digs (as in the case with the Virtual Ganjali Khan Project).


title: Virtual reality

text: Starting in the early 2020s, virtual reality has also been discussed as a technological setting that may support people's griefing process, based on digital recreations of deceased individuals. In 2021, this practice received substantial media attention following a South Korean TV documentary, which invited a griefing mother to interact with a virtual replica of her deceased daughter. Subsequently, scientists have summarized several potential implications of such endeavours, including its potential to facilitate adaptive mourning, but also many ethical challenges.


title: Virtual reality

text: Growing interest in the metaverse has resulted in organizational efforts to incorporate the many diverse applications of virtual reality into ecosystems like VIVERSE, reportedly offering connectivity between platforms for a wide range of uses.


title: Virtual reality

text: On February 21, 2019, DJ Marshmellow hosted a concert in Fortnite. Travis Scott performed on Fortnite on April 23, 2020. In June of that year, Jean Michel Jarre performed in VRChat. In July, Brendan Bradley released the free FutureStages web-based virtual reality venue for live events and concerts throughout the 2020 shutdown, Justin Bieber performed on November 18, 2021 in WaveXR. On December 2, 2021 Non-Player Character performed at The Mugar Omni Theater with audiences interacting with a live performer in both virtual reality and projected on the IMAX dome screen. Meta’s Foo Fighters Super Bowl VR concert performed on Venues. Post Malone performed in Venues starting July 15, 2022. Megan Thee Stallion performed on AmazeVR at AMC Theaters throughout 2022.


title: Virtual reality

text: On October 24, 2021, Billie Eilish performed on Oculus Venues. Pop group Imagine Dragons performed on June 15, 2022.


title: Virtual reality

text: There are many health and safety considerations of virtual reality. A number of unwanted symptoms have been caused by prolonged use of virtual reality, and these may have slowed proliferation of the technology. Most virtual reality systems come with consumer warnings, including: seizures; developmental issues in children; trip-and-fall and collision warnings; discomfort; repetitive stress injury; and interference with medical devices. Some users may experience twitches, seizures or blackouts while using VR headsets, even if they do not have a history of epilepsy and have never had blackouts or seizures before. One in 4,000 people, or .025%, may experience these symptoms. Motion sickness, eyestrain, headaches, and discomfort are the most prevalent short-term adverse effects. In addition, because of the virtual reality headsets' heavy weight, discomfort may be more likely among children. Therefore, children are advised against using VR headsets. Other problems may occur in physical interactions with one's environment. While wearing VR headsets, people quickly lose awareness of their real-world surroundings and may injure themselves by tripping over, or colliding with real-world objects.


title: Virtual reality

text: VR headsets may regularly cause eye fatigue, as does all screened technology, because people tend to blink less when watching screens, causing their eyes to become more dried out. There have been some concerns about VR headsets contributing to myopia, but although VR headsets sit close to the eyes, they may not necessarily contribute to nearsightedness if the focal length of the image being displayed is sufficiently far away.


title: Virtual reality

text: Virtual reality sickness (also known as cybersickness) occurs when a person's exposure to a virtual environment causes symptoms that are similar to motion sickness symptoms. Women are significantly more affected than men by headset-induced symptoms, at rates of around 77% and 33% respectively. The most common symptoms are general discomfort, headache, stomach awareness, nausea, vomiting, pallor, sweating, fatigue, drowsiness, disorientation, and apathy. For example, Nintendo's Virtual Boy received much criticism for its negative physical effects, including "dizziness, nausea, and headaches". These motion sickness symptoms are caused by a disconnect between what is being seen and what the rest of the body perceives. When the vestibular system, the body's internal balancing system, does not experience the motion that it expects from visual input through the eyes, the user may experience VR sickness. This can also happen if the VR system does not have a high enough frame rate, or if there is a lag between the body's movement and the onscreen visual reaction to it. Because approximately 25–40% of people experience some kind of VR sickness when using VR machines, companies are actively looking for ways to reduce VR sickness.


title: Virtual reality

text: In January 2022 "The Wall Street Journal" found that VR usage could lead to physical injuries including leg, hand, arm and shoulder injuries. VR usage has also been tied to incidents that resulted in neck injuries, and death.


title: Virtual reality

text: Children are becoming increasingly aware of VR, with the number in the USA having never heard of it dropping by half from Autumn 2016 (40%) to Spring 2017 (19%).


title: Virtual reality

text: A 2022 research report by Piper Sandler revealed that only 26% of U.S. teens own a VR device, 5% use it daily, while 48% of teen headset owners "seldom" use it. Of the teens who don't own a VR headset, 9% plan to buy one. 50% of surveyed teens are unsure about the metaverse or don't have any interest, and don't have any plans to purchase a VR headset.


title: Virtual reality

text: Studies show that young children, compared to adults, may respond cognitively and behaviorally to immersive VR in ways that differ from adults. VR places users directly into the media content, potentially making the experience very vivid and real for children. For example, children of 6–18 years of age reported higher levels of presence and "realness" of a virtual environment compared with adults 19–65 years of age.


title: Virtual reality

text: Studies on VR consumer behavior or its effect on children and a code of ethical conduct involving underage users are especially needed, given the availability of VR porn and violent content. Related research on violence in video games suggests that exposure to media violence may affect attitudes, behavior, and even self-concept. Self-concept is a key indicator of core attitudes and coping abilities, particularly in adolescents. Early studies conducted on observing versus participating in violent VR games suggest that physiological arousal and aggressive thoughts, but not hostile feelings, are higher for participants than for observers of the virtual reality game.


title: Virtual reality

text: Experiencing VR by children may further involve simultaneously holding the idea of the virtual world in mind while experiencing the physical world. Excessive usage of immersive technology that has very salient sensory features may compromise children's ability to maintain the rules of the physical world, particularly when wearing a VR headset that blocks out the location of objects in the physical world. Immersive VR can provide users with multisensory experiences that replicate reality or create scenarios that are impossible or dangerous in the physical world. Observations of 10 children experiencing VR for the first time suggested that 8-12-years-old kids were more confident to explore VR content when it was in a familiar situation, e.g. the children enjoyed playing in the kitchen context of Job Simulator, and enjoyed breaking rules by engaging in activities they are not allowed to do in reality, such as setting things on fire.


title: Virtual reality

text: The persistent tracking required by all VR systems makes the technology particularly useful for, and vulnerable to, mass surveillance. The expansion of VR will increase the potential and reduce the costs for information gathering of personal actions, movements and responses. Data from eye tracking sensors, which are projected to become a standard feature in virtual reality headsets, may indirectly reveal information about a user's ethnicity, personality traits, fears, emotions, interests, skills, and physical and mental health condition.


title: Schrödinger equation

text: The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, who postulated the equation in 1925, and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933.


title: Schrödinger equation

text: Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of a wave function, the quantum-mechanical characterization of an isolated physical system. The equation can be derived from the fact that the time-evolution operator must be unitary, and must therefore be generated by the exponential of a self-adjoint operator, which is the quantum Hamiltonian.


title: Schrödinger equation

text: The Schrödinger equation is not the only way to study quantum mechanical systems and make predictions. The other formulations of quantum mechanics include matrix mechanics, introduced by Werner Heisenberg, and the path integral formulation, developed chiefly by Richard Feynman. Paul Dirac incorporated matrix mechanics and the Schrödinger equation into a single formulation. When these approaches are compared, the use of the Schrödinger equation is sometimes called "wave mechanics".


title: Schrödinger equation

text: Introductory courses on physics or chemistry typically introduce the Schrödinger equation in a way that can be appreciated knowing only the concepts and notations of basic calculus, particularly derivatives with respect to space and time. A special case of the Schrödinger equation that admits a statement in those terms is the position-space Schrödinger equation for a single nonrelativistic particle in one dimension:


title: Schrödinger equation

text: Here, formula_2 is a wave function, a function that assigns a complex number to each point formula_3 at each time formula_4. The parameter formula_5 is the mass of the particle, and formula_6 is the "potential" that represents the environment in which the particle exists. The constant formula_7 is the imaginary unit, and formula_8 is the reduced Planck constant, which has units of action (energy multiplied by time).


title: Schrödinger equation

text: Broadening beyond this simple case, the mathematical formulation of quantum mechanics developed by Paul Dirac, David Hilbert, John von Neumann, and Hermann Weyl defines the state of a quantum mechanical system to be a vector formula_9 belonging to a (separable) Hilbert space formula_10. This vector is postulated to be normalized under the Hilbert space's inner product, that is, in Dirac notation it obeys formula_11. The exact nature of this Hilbert space is dependent on the system – for example, for describing position and momentum the Hilbert space is the space of complex square-integrable functions formula_12, while the Hilbert space for the spin of a single proton is simply the space of two-dimensional complex vectors formula_13 with the usual inner product.


title: Schrödinger equation

text: Physical quantities of interest – position, momentum, energy, spin – are represented by "observables", which are Hermitian (more precisely, self-adjoint) linear operators acting on the Hilbert space. A wave function can be an eigenvector of an observable, in which case it is called an eigenstate, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. More generally, a quantum state will be a linear combination of the eigenstates, known as a quantum superposition. When an observable is measured, the result will be one of its eigenvalues with probability given by the Born rule: in the simplest case the eigenvalue formula_14 is non-degenerate and the probability is given by formula_15, where formula_16 is its associated eigenvector. More generally, the eigenvalue is degenerate and the probability is given by formula_17, where formula_18 is the projector onto its associated eigenspace.


title: Schrödinger equation

text: A momentum eigenstate would be a perfectly monochromatic wave of infinite extent, which is not square-integrable. Likewise, a position eigenstate would be a Dirac delta distribution, not square-integrable and technically not a function at all. Consequently, neither can belong to the particle's Hilbert space. Physicists sometimes introduce fictitious "bases" for a Hilbert space comprising elements outside that space. These are invented for calculational convenience and do not represent physical states. Thus, a position-space wave function formula_2 as used above can be written as the inner product of a time-dependent state vector formula_20 with unphysical but convenient "position eigenstates" formula_21:


title: Schrödinger equation

text: The form of the Schrödinger equation depends on the physical situation. The most general form is the time-dependent Schrödinger equation, which gives a description of a system evolving with time:


title: Schrödinger equation

text: where formula_4 is time, formula_24 is the state vector of the quantum system (formula_25 being the Greek letter psi), and formula_26 is an observable, the Hamiltonian operator.


title: Schrödinger equation

text: The term "Schrödinger equation" can refer to both the general equation, or the specific nonrelativistic version. The general equation is indeed quite general, used throughout quantum mechanics, for everything from the Dirac equation to quantum field theory, by plugging in diverse expressions for the Hamiltonian. The specific nonrelativistic version is an approximation that yields accurate results in many situations, but only to a certain extent (see relativistic quantum mechanics and relativistic quantum field theory).


title: Schrödinger equation

text: To apply the Schrödinger equation, write down the Hamiltonian for the system, accounting for the kinetic and potential energies of the particles constituting the system, then insert it into the Schrödinger equation. The resulting partial differential equation is solved for the wave function, which contains information about the system. In practice, the square of the absolute value of the wave function at each point is taken to define a probability density function. For example, given a wave function in position space formula_2 as above, we have


title: Schrödinger equation

text: The time-dependent Schrödinger equation described above predicts that wave functions can form standing waves, called stationary states. These states are particularly important as their individual study later simplifies the task of solving the time-dependent Schrödinger equation for "any" state. Stationary states can also be described by a simpler form of the Schrödinger equation, the time-independent Schrödinger equation.


title: Schrödinger equation

text: where formula_29 is the energy of the system. This is only used when the Hamiltonian itself is not dependent on time explicitly. However, even in this case the total wave function is dependent on time as explained in the section on linearity below. In the language of linear algebra, this equation is an eigenvalue equation. Therefore, the wave function is an eigenfunction of the Hamiltonian operator with corresponding eigenvalue(s) formula_29.


title: Schrödinger equation

text: The Schrödinger equation is a linear differential equation, meaning that if two state vectors formula_31 and formula_32 are solutions, then so is any linear combination


title: Schrödinger equation

text: of the two where and are any complex numbers. Moreover, the sum can be extended for any number of state vectors. This property allows superpositions of quantum states to be solutions of the Schrödinger equation. Even more generally, it holds that a general solution to the Schrödinger equation can be found by taking a weighted sum over a basis of states. A choice often employed is the basis of energy eigenstates, which are solutions of the time-independent Schrödinger equation. In this basis, a time-dependent state vector formula_20 can be written as the linear combination


title: Schrödinger equation

text: where formula_36 are complex numbers and the vectors formula_37 are solutions of the time-independent equation formula_38.


title: Schrödinger equation

text: The operator formula_41 is known as the time-evolution operator, and it is unitary: it preserves the inner product between vectors in the Hilbert space. Unitarity is a general feature of time evolution under the Schrödinger equation. If the initial state is formula_42, then the state at a later time formula_4 will be given by


title: Schrödinger equation

text: for some unitary operator formula_45. Conversely, suppose that formula_45 is a continuous family of unitary operators parameterized by formula_4. Without loss of generality, the parameterization can be chosen so that formula_48 is the identity operator and that formula_49 for any formula_50. Then formula_45 depends upon the parameter formula_4 in such a way that


title: Schrödinger equation

text: for some self-adjoint operator formula_54, called the "generator" of the family formula_45. A Hamiltonian is just such a generator (up to the factor of Planck's constant that would be set to 1 in natural units).


title: Schrödinger equation

text: The Schrödinger equation is often presented using quantities varying as functions of position, but as a vector-operator equation it has a valid representation in any arbitrary complete basis of kets in Hilbert space. As mentioned above, "bases" that lie outside the physical Hilbert space are also employed for calculational purposes. This is illustrated by the "position-space" and "momentum-space" Schrödinger equations for a nonrelativistic, spinless particle. The Hilbert space for such a particle is the space of complex square-integrable functions on three-dimensional Euclidean space, and its Hamiltonian is the sum of a kinetic-energy term that is quadratic in the momentum operator and a potential-energy term:


title: Schrödinger equation

text: Writing formula_60 for a three-dimensional position vector and formula_61 for a three-dimensional momentum vector, the position-space Schrödinger equation is


title: Schrödinger equation

text: The momentum-space counterpart involves the Fourier transforms of the wave function and the potential:


title: Schrödinger equation

text: where formula_69 and formula_70 do not belong to the Hilbert space itself, but have well-defined inner products with all elements of that space.


title: Schrödinger equation

text: When restricted from three dimensions to one, the position-space equation is just the first form of the Schrödinger equation given above. The relation between position and momentum in quantum mechanics can be appreciated in a single dimension. In canonical quantization, the classical variables formula_3 and formula_72 are promoted to self-adjoint operators formula_73 and formula_74 that satisfy the canonical commutation relation


title: Schrödinger equation

text: so the action of the momentum operator formula_74 in the position-space representation is formula_78. Thus, formula_79 becomes a second derivative, and in three dimensions, the second derivative becomes the Laplacian formula_80.


title: Schrödinger equation

text: The canonical commutation relation also implies that the position and momentum operators are Fourier conjugates of each other. Consequently, functions originally defined in terms of their position dependence can be converted to functions of momentum using the Fourier transform. In solid-state physics, the Schrödinger equation is often written for functions of momentum, as Bloch's theorem ensures the periodic crystal lattice potential couples formula_81 with formula_82 for only discrete reciprocal lattice vectors formula_83. This makes it convenient to solve the momentum-space Schrödinger equation at each point in the Brillouin zone independently of the other points in the Brillouin zone.


title: Schrödinger equation

text: The Schrödinger equation is consistent with local probability conservation. Multiplying the Schrödinger equation on the right by the complex conjugate wave function, and multiplying the wave function to the left of the complex conjugate of the Schrödinger equation, and subtracting, gives the continuity equation for probability:


title: Schrödinger equation

text: If the Hamiltonian is not an explicit function of time, the equation is separable into a product of spatial and temporal parts. Solving the equation by separation of variables means seeking a solution of the form


title: Schrödinger equation

text: where formula_88 is a function of all the spatial coordinate(s) of the particle(s) constituting the system only, and formula_89 is a function of time only. Substituting this expression for formula_25 into the Schrödinger equation yields


title: Schrödinger equation

text: A solution of this type is called "stationary," since the only time dependence is a phase factor that cancels when the probability density is calculated via the Born rule.


title: Schrödinger equation

text: This generalizes to any number of particles in any number of dimensions (in a time-independent potential): the standing wave solutions of the time-dependent equation are the states with definite energy, instead of a probability distribution of different energies. In physics, these standing waves are called "stationary states" or "energy eigenstates"; in chemistry they are called "atomic orbitals" or "molecular orbitals". Superpositions of energy eigenstates change their properties according to the relative phases between the energy levels. The energy eigenstates form a basis: any wave function may be written as a sum over the discrete energy states or an integral over continuous energy states, or more generally as an integral over a measure. This is the spectral theorem in mathematics, and in a finite-dimensional state space it is just a statement of the completeness of the eigenvectors of a Hermitian matrix.


title: Schrödinger equation

text: Separation of variables can also be a useful method for the time-independent Schrödinger equation. For example, depending on the symmetry of the problem, the Cartesian axes might be separated,


title: Schrödinger equation

text: The particle in a one-dimensional potential energy box is the most mathematically simple example where restraints lead to the quantization of energy levels. The box is defined as having zero potential energy "inside" a certain region and infinite potential energy "outside". For the one-dimensional case in the formula_3 direction, the time-independent Schrödinger equation may be written


title: Schrödinger equation

text: with state formula_98 in this case having energy formula_29 coincident with the kinetic energy of the particle.


title: Schrödinger equation

text: The infinite potential walls of the box determine the values of formula_102 and formula_103 at formula_104 and formula_105 where formula_98 must be zero. Thus, at formula_104,


title: Schrödinger equation

text: in which formula_112 cannot be zero as this would conflict with the postulate that formula_98 has norm 1. Therefore, since formula_114, formula_115 must be an integer multiple of formula_116,


title: Schrödinger equation

text: A finite potential well is the generalization of the infinite potential well problem to potential wells having finite depth. The finite potential well problem is mathematically more complicated than the infinite particle-in-a-box problem as the wave function is not pinned to zero at the walls of the well. Instead, the wave function must satisfy more complicated mathematical boundary conditions as it is nonzero in regions outside the well. Another related problem is that of the rectangular potential barrier, which furnishes a model for the quantum tunneling effect that plays an important role in the performance of modern technologies such as flash memory and scanning tunneling microscopy.


title: Schrödinger equation

text: where formula_121 is the displacement and formula_122 the angular frequency. Furthermore, it can be used to describe approximately a wide variety of other systems, including vibrating atoms, molecules, and atoms or ions in lattices, and approximating other potentials near equilibrium points. It is also the basis of perturbation methods in quantum mechanics.


title: Schrödinger equation

text: where formula_124, and the functions formula_125 are the Hermite polynomials of order formula_126. The solution set may be generated by


title: Schrödinger equation

text: The case formula_129 is called the ground state, its energy is called the zero-point energy, and the wave function is a Gaussian.


title: Schrödinger equation

text: The harmonic oscillator, like the particle in a box, illustrates the generic feature of the Schrödinger equation that the energies of bound eigenstates are discretized.


title: Schrödinger equation

text: where formula_131 is the electron charge, formula_132 is the position of the electron relative to the nucleus, formula_133 is the magnitude of the relative position, the potential term is due to the Coulomb interaction, wherein formula_134 is the permittivity of free space and


title: Schrödinger equation

text: is the 2-body reduced mass of the hydrogen nucleus (just a proton) of mass formula_136 and the electron of mass formula_137. The negative sign arises in the potential term since the proton and electron are oppositely charged. The reduced mass in place of the electron mass is used since the electron and proton together orbit each other about a common centre of mass, and constitute a two-body problem to solve. The motion of the electron is of principal interest here, so the equivalent one-body problem is the motion of the electron using the reduced mass.


title: Schrödinger equation

text: The Schrödinger equation for a hydrogen atom can be solved by separation of variables. In this case, spherical polar coordinates are the most convenient. Thus,


title: Schrödinger equation

text: where are radial functions and formula_139 are spherical harmonics of degree formula_140 and order formula_141. This is the only atom for which the Schrödinger equation has been solved for exactly. Multi-electron atoms require approximate methods. The family of solutions are:


title: Schrödinger equation

text: It is typically not possible to solve the Schrödinger equation exactly for situations of physical interest. Accordingly, approximate solutions are obtained using techniques like variational methods and WKB approximation. It is also common to treat a problem of interest as a small modification to a problem that can be solved exactly, a method known as perturbation theory.


title: Schrödinger equation

text: One simple way to compare classical to quantum mechanics is to consider the time-evolution of the "expected" position and "expected" momentum, which can then be compared to the time-evolution of the ordinary position and momentum in classical mechanics. The quantum expectation values satisfy the Ehrenfest theorem. For a one-dimensional quantum particle moving in a potential formula_150, the Ehrenfest theorem says


title: Schrödinger equation

text: Although the first of these equations is consistent with the classical behavior, the second is not: If the pair formula_152 were to satisfy Newton's second law, the right-hand side of the second equation would have to be


title: Schrödinger equation

text: which is typically not the same as formula_154. For a general formula_155, therefore, quantum mechanics can lead to predictions where expectation values do not mimic the classical behavior. In the case of the quantum harmonic oscillator, however, formula_155 is linear and this distinction disappears, so that in this very special case, the expected position and expected momentum do exactly follow the classical trajectories.


title: Schrödinger equation

text: For general systems, the best we can hope for is that the expected position and momentum will "approximately" follow the classical trajectories. If the wave function is highly concentrated around a point formula_157, then formula_158 and formula_159 will be "almost" the same, since both will be approximately equal to formula_160. In that case, the expected position and expected momentum will remain very close to the classical trajectories, at least for as long as the wave function remains highly localized in position.


title: Schrödinger equation

text: where formula_163 is the classical action and formula_164 is the Hamiltonian function (not operator). Here the generalized coordinates formula_165 for formula_166 (used in the context of the HJE) can be set to the position in Cartesian coordinates as formula_167.


title: Schrödinger equation

text: where formula_169 is the probability density, into the Schrödinger equation and then taking the limit formula_170 in the resulting equation yield the Hamilton–Jacobi equation.


title: Schrödinger equation

text: Wave functions are not always the most convenient way to describe quantum systems and their behavior. When the preparation of a system is only imperfectly known, or when the system under investigation is a part of a larger whole, density matrices may be used instead. A density matrix is a positive semi-definite operator whose trace is equal to 1. (The term "density operator" is also used, particularly when the underlying Hilbert space is infinite-dimensional.) The set of all density matrices is convex, and the extreme points are the operators that project onto vectors in the Hilbert space. These are the density-matrix representations of wave functions; in Dirac notation, they are written formula_171


title: Schrödinger equation

text: where the brackets denote a commutator. This is variously known as the von Neumann equation, the Liouville–von Neumann equation, or just the Schrödinger equation for density matrices. If the Hamiltonian is time-independent, this equation can be easily solved to yield


title: Schrödinger equation

text: More generally, if the unitary operator formula_45 describes wave function evolution over some time interval, then the time evolution of a density matrix over that same interval is given by


title: Schrödinger equation

text: The one-particle Schrödinger equation described above is valid essentially in the nonrelativistic domain. For one reason, it is essentially invariant under Galilean transformations, which comprise the symmetry group of Newtonian dynamics. Moreover, processes that change particle number are natural in relativity, and so an equation for one particle (or any fixed number thereof) can only be of limited use. A more general form of the Schrödinger equation that also applies in relativistic situations can be formulated within quantum field theory (QFT), a framework that allows the combination of quantum mechanics with special relativity. The region in which both simultaneously apply may be described by relativistic quantum mechanics. Such descriptions may use time evolution generated by a Hamiltonian operator, as in the Schrödinger functional method.


title: Schrödinger equation

text: Attempts to combine quantum physics with special relativity began with building relativistic wave equations from the relativistic energy–momentum relation


title: Schrödinger equation

text: instead of nonrelativistic energy equations. The Klein–Gordon equation and the Dirac equation are two such equations. The Klein–Gordon equation,


title: Schrödinger equation

text: was the first such equation to be obtained, even before the nonrelativistic one-particle Schrödinger equation, and applies to massive spinless particles. Historically, Dirac obtained the Dirac equation by seeking a differential equation that would be first-order in both time and space, a desirable property for a relativistic theory. Taking the "square root" of the left-hand side of the Klein–Gordon equation in this way required factorizing it into a product of two operators, which Dirac wrote using 4 × 4 matrices formula_178. Consequently, the wave function also became a four-component function, governed by the Dirac equation that, in free space, read


title: Schrödinger equation

text: This has again the form of the Schrödinger equation, with the time derivative of the wave function being given by a Hamiltonian operator acting upon the wave function. Including influences upon the particle requires modifying the Hamiltonian operator. For example, the Dirac Hamiltonian for a particle of mass and electric charge in an electromagnetic field (described by the electromagnetic potentials and ) is:


title: Schrödinger equation

text: in which the and are the Dirac gamma matrices related to the spin of the particle. The Dirac equation is true for all particles, and the solutions to the equation are spinor fields with two components corresponding to the particle and the other two for the antiparticle.


title: Schrödinger equation

text: For the Klein–Gordon equation, the general form of the Schrödinger equation is inconvenient to use, and in practice the Hamiltonian is not expressed in an analogous way to the Dirac Hamiltonian. The equations for relativistic quantum fields, of which the Klein–Gordon and Dirac equations are two examples, can be obtained in other ways, such as starting from a Lagrangian density and using the Euler–Lagrange equations for fields, or using the representation theory of the Lorentz group in which certain representations can be used to fix the equation for a free particle of given spin (and mass).


title: Schrödinger equation

text: In general, the Hamiltonian to be substituted in the general Schrödinger equation is not just a function of the position and momentum operators (and possibly time), but also of spin matrices. Also, the solutions to a relativistic wave equation, for a massive particle of spin , are complex-valued spinor fields.


title: Schrödinger equation

text: As originally formulated, the Dirac equation is an equation for a single quantum particle, just like the single-particle Schrödinger equation with wave function This is of limited use in relativistic quantum mechanics, where particle number is not fixed. Heuristically, this complication can be motivated by noting that mass–energy equivalence implies material particles can be created from energy. A common way to address this in QFT is to introduce a Hilbert space where the basis states are labeled by particle number, a so-called Fock space. The Schrödinger equation can then be formulated for quantum states on this Hilbert space. However, because the Schrödinger equation picks out a preferred time axis, the Lorentz invariance of the theory is no longer manifest, and accordingly, the theory is often formulated in other ways.


title: Schrödinger equation

text: Following Max Planck's quantization of light (see black-body radiation), Albert Einstein interpreted Planck's quanta to be photons, particles of light, and proposed that the energy of a photon is proportional to its frequency, one of the first signs of wave–particle duality. Since energy and momentum are related in the same way as frequency and wave number in special relativity, it followed that the momentum formula_72 of a photon is inversely proportional to its wavelength formula_14, or proportional to its wave number formula_103:


title: Schrödinger equation

text: where formula_185 is Planck's constant and formula_186 is the reduced Planck constant. Louis de Broglie hypothesized that this is true for all particles, even particles which have mass such as electrons. He showed that, assuming that the matter waves propagate along with their particle counterparts, electrons form standing waves, meaning that only certain discrete rotational frequencies about the nucleus of an atom are allowed.


title: Schrödinger equation

text: These quantized orbits correspond to discrete energy levels, and de Broglie reproduced the Bohr model formula for the energy levels. The Bohr model was based on the assumed quantization of angular momentum formula_187 according to


title: Schrödinger equation

text: According to de Broglie, the electron is described by a wave, and a whole number of wavelengths must fit along the circumference of the electron's orbit:


title: Schrödinger equation

text: This approach essentially confined the electron wave in one dimension, along a circular orbit of radius formula_190.


title: Schrödinger equation

text: In 1921, prior to de Broglie, Arthur C. Lunn at the University of Chicago had used the same argument based on the completion of the relativistic energy–momentum 4-vector to derive what we now call the de Broglie relation. Unlike de Broglie, Lunn went on to formulate the differential equation now known as the Schrödinger equation and solve for its energy eigenvalues for the hydrogen atom. Unfortunately the paper was rejected by the "Physical Review", as recounted by Kamen.


title: Schrödinger equation

text: Following up on de Broglie's ideas, physicist Peter Debye made an offhand comment that if particles behaved as waves, they should satisfy some sort of wave equation. Inspired by Debye's remark, Schrödinger decided to find a proper 3-dimensional wave equation for the electron. He was guided by William Rowan Hamilton's analogy between mechanics and optics, encoded in the observation that the zero-wavelength limit of optics resembles a mechanical system—the trajectories of light rays become sharp tracks that obey Fermat's principle, an analog of the principle of least action.


title: Schrödinger equation

text: However, by that time, Arnold Sommerfeld had refined the Bohr model with relativistic corrections. Schrödinger used the relativistic energy–momentum relation to find what is now known as the Klein–Gordon equation in a Coulomb potential (in natural units):


title: Schrödinger equation

text: He found the standing waves of this relativistic equation, but the relativistic corrections disagreed with Sommerfeld's formula. Discouraged, he put away his calculations and secluded himself with a mistress in a mountain cabin in December 1925.


title: Schrödinger equation

text: While at the cabin, Schrödinger decided that his earlier nonrelativistic calculations were novel enough to publish and decided to leave off the problem of relativistic corrections for the future. Despite the difficulties in solving the differential equation for hydrogen (he had sought help from his friend the mathematician Hermann Weyl) Schrödinger showed that his nonrelativistic version of the wave equation produced the correct spectral energies of hydrogen in a paper published in 1926. Schrödinger computed the hydrogen spectral series by treating a hydrogen atom's electron as a wave formula_193, moving in a potential well formula_150, created by the proton. This computation accurately reproduced the energy levels of the Bohr model.


title: Schrödinger equation

text: The Schrödinger equation details the behavior of formula_25 but says nothing of its "nature". Schrödinger tried to interpret the real part of formula_196 as a charge density, and then revised this proposal, saying in his next paper that the modulus squared of formula_25 is a charge density. This approach was, however, unsuccessful. In 1926, just a few days after this paper was published, Max Born successfully interpreted formula_25 as the probability amplitude, whose modulus squared is equal to probability density. Later, Schrödinger himself explained this interpretation as follows:


title: Schrödinger equation

text: The Schrödinger equation provides a way to calculate the wave function of a system and how it changes dynamically in time. However, the Schrödinger equation does not directly say "what," exactly, the wave function is. The meaning of the Schrödinger equation and how the mathematical entities in it relate to physical reality depends upon the interpretation of quantum mechanics that one adopts.


title: Schrödinger equation

text: In the views often grouped together as the Copenhagen interpretation, a system's wave function is a collection of statistical information about that system. The Schrödinger equation relates information about the system at one time to information about it at another. While the time-evolution process represented by the Schrödinger equation is continuous and deterministic, in that knowing the wave function at one instant is in principle sufficient to calculate it for all future times, wave functions can also change discontinuously and stochastically during a measurement. The wave function changes, according to this school of thought, because new information is available. The post-measurement wave function generally cannot be known prior to the measurement, but the probabilities for the different possibilities can be calculated using the Born rule. Other, more recent interpretations of quantum mechanics, such as relational quantum mechanics and QBism also give the Schrödinger equation a status of this sort.


title: Schrödinger equation

text: Schrödinger himself suggested in 1952 that the different terms of a superposition evolving under the Schrödinger equation are "not alternatives but all really happen simultaneously". This has been interpreted as an early version of Everett's many-worlds interpretation. This interpretation, formulated independently in 1956, holds that "all" the possibilities described by quantum theory "simultaneously" occur in a multiverse composed of mostly independent parallel universes. This interpretation removes the axiom of wave function collapse, leaving only continuous evolution under the Schrödinger equation, and so all possible states of the measured system and the measuring apparatus, together with the observer, are present in a real physical quantum superposition. While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities, because we don't observe the multiverse as a whole, but only one parallel universe at a time. Exactly how this is supposed to work has been the subject of much debate. Why we should assign probabilities at all to outcomes that are certain to occur in some worlds, and why should the probabilities be given by the Born rule? Several ways to answer these questions in the many-worlds framework have been proposed, but there is no consensus on whether they are successful.


title: Schrödinger equation

text: Bohmian mechanics reformulates quantum mechanics to make it deterministic, at the price of making it explicitly nonlocal (a price exacted by Bell's theorem). It attributes to each physical system not only a wave function but in addition a real position that evolves deterministically under a nonlocal guiding equation. The evolution of a physical system is given at all times by the Schrödinger equation together with the guiding equation.


title: Victoria (Australia)

text: Victoria is a state in southeastern Australia. It is the second-smallest state with a land area of , the second most populated state (after New South Wales) with a population of over 6.5 million, and the most densely populated state in Australia (28 per km). Victoria is bordered by New South Wales to the north and South Australia to the west, and is bounded by the Bass Strait to the south (with the exception of a small land border with Tasmania located along Boundary Islet), the Great Australian Bight portion of the Southern Ocean to the southwest, and the Tasman Sea (a marginal sea of the South Pacific Ocean) to the southeast. The state encompasses a range of climates and geographical features from its temperate coastal and central regions to the Victorian Alps in the northeast and the semi-arid north-west.


title: Victoria (Australia)

text: The majority of the Victorian population is concentrated in the central-south area surrounding Port Phillip Bay, and in particular within the metropolitan area of Greater Melbourne, Victoria's state capital and largest city and also Australia's second-largest city, where over three quarters of the Victorian population live. The state is home to four of Australia's 20 largest cities: Melbourne, Geelong, Ballarat and Bendigo. The population is culturally diverse, with 35.1% of inhabitants being immigrants.


title: Victoria (Australia)

text: Victoria is home to numerous Aboriginal groups, including the Boonwurrung, the Bratauolung, the Djadjawurrung, the Gunai, the Gunditjmara, the Taungurung, the Wathaurong, the Wurundjeri, and the Yorta Yorta. There were more than 30 Aboriginal languages spoken in the area prior to European colonisation. In 1770 James Cook claimed the east coast of the Australian continent for the Kingdom of Great Britain, and from 1788 the area that is now Victoria was a part of the colony of New South Wales. The first European settlement in the area occurred in 1803 at Sullivan Bay. Much of what is now Victoria was included in 1836 in the Port Phillip District of New South Wales. Named in honour of Queen Victoria, Victoria was separated from New South Wales and established as a separate Crown colony in 1851, achieving responsible government in 1855. The Victorian gold rush in the 1850s and 1860s significantly increased Victoria's population and wealth. By the time of Australian Federation in 1901, Melbourne had become the largest city in Australasia, and served as the federal capital of Australia until Canberra was opened in 1927. The state continued to grow strongly through various periods of the 20th and early 21st centuries as a result of high levels of international and interstate migration.


title: Victoria (Australia)

text: Victoria has 38 seats in the Australian House of Representatives and 12 seats in the Australian Senate. At state level, the Parliament of Victoria consists of the Legislative Assembly and the Legislative Council. The Labor Party, led by Daniel Andrews as premier, has governed Victoria since 2014. The Governor of Victoria, the representative of the Monarchy of Australia in the state, is currently Linda Dessau. Victoria is divided into 79 local government areas, as well as several unincorporated areas which the state administers directly.


title: Victoria (Australia)

text: Victoria's economy is the second-largest among Australian states and is highly diversified, with service sectors predominating. Culturally, Melbourne hosts a number of museums, art galleries, and theatres, and is also described as the world's sporting capital, and the spiritual home of Australian cricket and Australian rules football.


title: Victoria (Australia)

text: The state of Victoria was originally home to many Aboriginal Australian nations that had occupied the land for tens of thousands of years before European settlement. According to Gary Presland, Aboriginal people have lived in Victoria for about 40,000 years, living a semi-nomadic existence of fishing, hunting and gathering, and farming eels.


title: Victoria (Australia)

text: At the Keilor Archaeological Site a human hearth excavated in 1971 was radiocarbon-dated to about 31,000 years BP, making Keilor one of the earliest sites of human habitation in Australia. A cranium found at the site has been dated at between 12,000 and 14,700 years BP.


title: Victoria (Australia)

text: Archaeological sites in Tasmania and on the Bass Strait Islands have been dated to between 20,000 – 35,000 years ago, when sea levels were 130 metres below present level allowing First Nations Peoples to move across the region of southern Victoria and on to the land bridge of the Bassian plain to Tasmania by at least 35,000 years ago.


title: Victoria (Australia)

text: During the Ice Age about 20,000 years BP, the area now the bay of Port Phillip would have been dry land, and the Yarra and Werribee river would have joined to flow through the heads then south and south west through the Bassian plain before meeting the ocean to the west. Tasmania and the Bass Strait islands became separated from mainland Australia around 12,000 BP, when the sea level was approximately 50m below present levels. Port Phillip was flooded by post-glacial rising sea levels between 8000 and 6000 years ago.


title: Victoria (Australia)

text: Oral history and creation stories from the Wada wurrung, Woiwurrung and Bun wurrung languages describe the flooding of the bay. Hobsons Bay was once a kangaroo hunting ground. Creation stories describe how Bunjil was responsible for the formation of the bay, or the bay was flooded when the Yarra river was created.


title: Victoria (Australia)

text: Victoria, like Queensland, was named after Queen Victoria, who had been on the British throne for 14 years when the colony was established in 1851.


title: Victoria (Australia)

text: After the founding of the colony of New South Wales in 1788, Australia was divided into an eastern half named New South Wales and a western half named New Holland, under the administration of the colonial government in Sydney. The first British settlement in the area later known as Victoria was established in October 1803 under Lieutenant-Governor David Collins at Sullivan Bay on Port Phillip. It consisted of 402 people (five government officials, nine officers of marines, two drummers, and 39 privates, five soldiers' wives and a child, 307 convicts, 17 convicts' wives, and seven children). They had been sent from England in under the command of Captain Daniel Woodriff, principally out of fear that the French, who had been exploring the area, might establish their own settlement and thereby challenge British rights to the continent.


title: Victoria (Australia)

text: In 1826, Colonel Stewart, Captain Samuel Wright, and Lieutenant Burchell were sent in (Captain Wetherall) and the brigs "Dragon" and "Amity", took a number of convicts and a small force composed of detachments of the 3rd and 93rd regiments. The expedition landed at Settlement Point (now Corinella), on the eastern side of Western Port Bay, which was the headquarters until the abandonment of Western Port at the insistence of Governor Darling about 12 months afterwards.


title: Victoria (Australia)

text: Victoria's next settlement was at Portland, on the south west coast of what is now Victoria. Edward Henty settled Portland Bay in 1834.


title: Victoria (Australia)

text: Melbourne was founded in 1835 by John Batman, who set up a base in Indented Head, and John Pascoe Fawkner. From settlement, the region around Melbourne was known as the Port Phillip District, a separately administered part of New South Wales. Shortly after, the site now known as Geelong was surveyed by Assistant Surveyor W. H. Smythe, three weeks after Melbourne. And in 1838, Geelong was officially declared a town, despite earlier European settlements dating back to 1826.


title: Victoria (Australia)

text: On 6 June 1835, just under two years before Melbourne was officially recognised as a settlement, John Batman, the leader of the Port Phillip Association presented Wurundjeri Elders with a land use agreement. This document, now referred to as the Batman treaty, was later given to the British government to claim that local Aboriginal people had given Batman access to their land in exchange for goods and rations. Today, the meaning and interpretation of this treaty is contested. Some argue it was pretence for taking Aboriginal land in exchange for trinkets, while others argue it was significant in that it sought to recognise Aboriginal land rights.


title: Victoria (Australia)

text: The exact location of the meeting between Batman and the Kulin Ngurungaeta (head clan-men) with whom he made the treaty is unknown, although it is believed to have been by the Merri Creek. According to historian Meyer Eidelson, it is generally believed to have occurred on the Merri near modern-day Rushall Station.


title: Victoria (Australia)

text: On 1 July 1851, writs were issued for the election of the first Victorian Legislative Council, and the absolute independence of Victoria from New South Wales was established proclaiming a new Colony of Victoria. Days later, still in 1851 gold was discovered near Ballarat, and subsequently at Bendigo. Later discoveries occurred at many sites across Victoria. This triggered one of the largest gold rushes the world has ever seen. The colony grew rapidly in both population and economic power. In 10 years, the population of Victoria increased sevenfold from 76,000 to 540,000. All sorts of gold records were produced, including the "richest shallow alluvial goldfield in the world" and the largest gold nugget. In the decade 1851–1860 Victoria produced 20 million ounces of gold, one-third of the world's output.


title: Victoria (Australia)

text: Immigrants arrived from all over the world to search for gold, especially from Ireland and China. By 1857, 26,000 Chinese miners worked in Victoria, and their legacy is particularly strong in Bendigo and its environs.


title: Victoria (Australia)

text: In 1854 at Ballarat, an armed rebellion against the government of Victoria was made by miners protesting against mining taxes (the "Eureka Stockade"). This was crushed by British troops, but the confrontation persuaded the colonial authorities to reform the administration of mining concessions (reducing the hated mining licence fees) and extend the electoral franchise. The following year, the Imperial Parliament granted Victoria responsible government with the passage of the Colony of Victoria Act 1855. Some of the leaders of the Eureka rebellion went on to become members of the Victorian Parliament.


title: Victoria (Australia)

text: In 1857, reflecting the growing presence of Irish Catholic immigrants, John O'Shanassy became the colony's second Premier with the former Young Irelander, Charles Gavan Duffy as his deputy. Melbourne's Protestant establishment was ill-prepared "to countenance so startling a novelty". In 1858–59, "Melbourne Punch" cartoons linked Duffy and O'Shanassy to the terrors of the French Revolution.


title: Victoria (Australia)

text: In 1862 Duffy's Land Act attempted, but failed, through a system of extended pastoral licences, to break the land-holding monopoly of the so-called "squatter" class. In 1871, having led, on behalf of small farmers, opposition to Premier Sir James McCulloch's land tax, Duffy, himself, was briefly Premier.


title: Victoria (Australia)

text: In 1893 widespread bank failures brought to an end a sustained period of prosperity and of increasingly wild speculation in land and construction. Melbourne nonetheless retained, as the legacy of the gold rush, its status as Australia's primary financial centre and largest city.


title: Victoria (Australia)

text: In 1901, Victoria became a state in the Commonwealth of Australia. While Canberra was being built, Melbourne served until 1927 as country's first federal capital.


title: Victoria (Australia)

text: Victoria's northern border follows a straight line from Cape Howe to the start of the Murray River and then follows the Murray River as the remainder of the northern border. On the Murray River, the border is the southern bank of the river. This precise definition was not established until 1980, when a ruling by Justice Ninian Stephen of the High Court of Australia settled the question as to which state had jurisdiction in the unlawful death of a man on an island in the middle of the river. The ruling clarified that no part of the watercourse is in Victoria. The border also rests at the southern end of the Great Dividing Range, which stretches along the east coast and terminates west of Ballarat. It is bordered by South Australia to the west and shares Australia's shortest land border with Tasmania. The official border between Victoria and Tasmania is at 39°12' S, which passes through Boundary Islet in the Bass Strait for 85 metres.


title: Victoria (Australia)

text: Victoria contains many topographically, geologically and climatically diverse areas, ranging from the wet, temperate climate of Gippsland in the southeast to the snow-covered Victorian alpine areas which rise to almost , with Mount Bogong the highest peak at . There are extensive semi-arid plains to the west and northwest. There is an extensive series of river systems in Victoria. Most notable is the Murray River system. Other rivers include: Ovens River, Goulburn River, Patterson River, King River, Campaspe River, Loddon River, Wimmera River, Elgin River, Barwon River, Thomson River, Snowy River, Latrobe River, Yarra River, Maribyrnong River, Mitta River, Hopkins River, Merri River and Kiewa River. The state symbols include the pink heath (state flower), Leadbeater's possum (state animal) and the helmeted honeyeater (state bird). Ecological communities include Victorian Volcanic Plain grasslands, Northern Plains Grassland and Gippsland Plains Grassy Woodland, all of which are critically endangered.


title: Victoria (Australia)

text: According to Geoscience Australia, the geographic centre of Victoria is located in Mandurang at 36° 51' 15"S, 144° 16' 52" E. The small rural locality is located 10 km (6 mi) south of Bendigo. Due to its central location and the region's historical ties to the gold rush, the town is widely regarded as the "Heart of Gold".


title: Victoria (Australia)

text: The state's capital, Melbourne, contains about 70% of the state's population and dominates its economy, media, and culture. For other cities and towns, see list of localities (Victoria) and local government areas of Victoria.


title: Victoria (Australia)

text: Urban centres are defined by the Australian Bureau of Statistics as being a population cluster of 1,000 or more people. The below figures broadly represent the populations of the contiguous built-up areas of each city.


title: Victoria (Australia)

text: Victoria has a varied climate despite its small size. It ranges from semi-arid temperate with hot summers in the north-west, to temperate and cool along the coast. Victoria's main land feature, the Great Dividing Range, produces a cooler, mountain climate in the centre of the state. Winters along the coast of the state, particularly around Melbourne, are relatively mild ("see chart at right)".


title: Victoria (Australia)

text: The coastal plain south of the Great Dividing Range has Victoria's mildest climate. Air from the Southern Ocean helps reduce the heat of summer and the cold of winter. Melbourne and other large cities are located in this temperate region.


title: Victoria (Australia)

text: The Mallee and upper Wimmera are Victoria's warmest regions with hot winds blowing from nearby semi-deserts. Average temperatures exceed during summer and in winter. Except at cool mountain elevations, the inland monthly temperatures are warmer than around Melbourne (see chart). Victoria's highest maximum temperature of was recorded in Hopetoun on 7 February 2009, during the 2009 southeastern Australia heat wave.


title: Victoria (Australia)

text: The Victorian Alps in the northeast are the coldest part of Victoria. The Alps are part of the Great Dividing Range mountain system extending east–west through the centre of Victoria. Average temperatures are less than in winter and below in the highest parts of the ranges. The state's lowest minimum temperature of was recorded at Omeo on 15 June 1965, and again at Falls Creek on 3 July 1970. Temperature extremes for the state are listed in the table below:


title: Victoria (Australia)

text: Rainfall in Victoria increases from south to the northeast, with higher averages in areas of high altitude. Mean annual rainfall exceeds in some parts of the northeast but is less than in the Mallee.


title: Victoria (Australia)

text: Rain is heaviest in the Otway Ranges and Gippsland in southern Victoria and in the mountainous northeast. Snow generally falls only in the mountains and hills in the centre of the state. Rain falls most frequently in winter, but summer precipitation is heavier. Rainfall is most reliable in Gippsland and the Western District, making them both leading farming areas. Victoria's highest recorded daily rainfall was at Tidal River in Wilsons Promontory National Park on 23 March 2011.


title: Victoria (Australia)

text: At December 2021 Victoria had a population of 6,559,941. The Australian Bureau of Statistics estimates that the population may well reach 7.2 million by 2050.


title: Victoria (Australia)

text: Victoria's founding Anglo-Celtic population has been supplemented by successive waves of migrants from Southern and Eastern Europe, Asia and, most recently, Africa and the Middle East. Victoria's population is ageing in proportion with the average of the remainder of the Australian population.


title: Victoria (Australia)

text: About 72% of Victorians are Australian-born. This figure falls to around 66% in Melbourne but rises to higher than 95% in some rural areas in the north west of the state. Less than 1% of Victorians identify themselves as Aboriginal.


title: Victoria (Australia)

text: More than 75% of Victorians live in Melbourne, located in the state's south. The greater Melbourne metropolitan area is home to an estimated 4,850,740 people. Urban centres outside Melbourne include Geelong, Ballarat, Bendigo, Shepparton, Mildura, Warrnambool, Wodonga and the Latrobe Valley.


title: Victoria (Australia)

text: Victoria is Australia's most urbanised state: nearly 90% of residents living in cities and towns. State Government efforts to decentralise population have included an official campaign run since 2003 to encourage Victorians to settle in regional areas, however Melbourne continues to rapidly outpace these areas in terms of population growth.


title: Victoria (Australia)

text: 0.8% of the population, or 47,788 people, identified as Indigenous Australians (Aboriginal Australians and Torres Strait Islanders) in 2016.


title: Victoria (Australia)

text: At the 2016 census, 64.9% of residents were born in Australia. The other most common countries of birth were England (2.9%), India (2.9%), Mainland China (2.7%), New Zealand (1.6%) and Vietnam (1.4%).


title: Victoria (Australia)

text: As of the 2016 census, 72.2% of Victorians speak English at home. Speakers of other languages include Mandarin (3.2%), Italian (1.9%), Greek (1.9%), Vietnamese (1.7%), and Arabic (1.3%).


title: Victoria (Australia)

text: In the 2016 Census, 47.9% of Victorians described themselves as Christian, 10.6% stated that they followed other religions and 32.1% stated that they had no religion or held secular or other spiritual beliefs. In the survey, 31.7% of Victorians stated they had no religion, Roman Catholics were 23.2%, 9.4% did not answer the question, 9% were Anglican and 3.5% were Eastern Orthodox.


title: Victoria (Australia)

text: In 2017 the proportion of couples marrying in a civil ceremony in Victoria was 77.3%; the other 22.7% were married in a religious ceremony.


title: Victoria (Australia)

text: The government predicts that nearly a quarter of Victorians will be aged over 60 by 2021. The 2016 census revealed that Australian median age has crept upward from 35 to 37 since 2001, which reflects the population growth peak of 1969–72. In 2017, Victoria recorded a TFR of 1.724.


title: Victoria (Australia)

text: In the year ending September 2020, the statistics were skewed by the introduction of six new public safety offences relating to the COVID-19 pandemic in Australia. Total offences numbered 551,710, with 32,713 of these were breaches of Chief Health Officer Directions. The total offences occurred at a rate of 8,227 per 100,000 people, up 4.4% on the previous year. While there have been some dips along the way, the rate of recorded offences have increased year on year since 2011, when the figure was 6,937.7 offences per 100,000 people.


title: Victoria (Australia)

text: Victoria has a parliamentary form of government based on the Westminster System. Legislative power resides in the Parliament consisting of the Governor (the representative of the King), the executive (the Government), and two legislative chambers. The Parliament of Victoria consists of the lower house Legislative Assembly, the upper house Legislative Council and the monarch of Australia.


title: Victoria (Australia)

text: Eighty-eight members of the Legislative Assembly are elected to four-year terms from single-member electorates.


title: Victoria (Australia)

text: In November 2006, the Victorian Legislative Council elections were held under a new multi-member proportional representation system. The State of Victoria was divided into eight electorates with each electorate represented by five representatives elected by Single Transferable Vote. The total number of upper house members was reduced from 44 to 40 and their term of office is now the same as the lower house members—four years. Elections for the Victorian Parliament are now fixed and occur in November every four years. Prior to the 2006 election, the Legislative Council consisted of 44 members elected to eight-year terms from 22 two-member electorates.


title: Victoria (Australia)

text: The Premier of Victoria is the leader of the political party or coalition with the most seats in the Legislative Assembly. The Premier is the public face of government and, with cabinet, sets the legislative and political agenda. Cabinet consists of representatives elected to either house of parliament. It is responsible for managing areas of government that are not exclusively vested in the Commonwealth, by the Australian Constitution, such as education, health and law enforcement. The current Premier of Victoria is Daniel Andrews.


title: Victoria (Australia)

text: Executive authority is vested in the Governor of Victoria who represents and is appointed by the monarch of Australia. The post is usually filled by a retired prominent Victorian. The governor acts on the advice of the premier and cabinet. The current Governor of Victoria is Linda Dessau.


title: Victoria (Australia)

text: Victoria has a written constitution enacted in 1975, but based on the 1855 colonial constitution, passed by the United Kingdom Parliament as the "Victoria Constitution Act 1855", which establishes the Parliament as the state's law-making body for matters coming under state responsibility. The Victorian Constitution can be amended by the Parliament of Victoria, except for certain "entrenched" provisions that require either an absolute majority in both houses, a three-fifths majority in both houses, or the approval of the Victorian people in a referendum, depending on the provision.


title: Victoria (Australia)

text: Victorians, and Melburnians in particular, are considered by some analysts to be more progressive than other Australians. The state recorded the highest "Yes" votes of any state in the republic referendum and same-sex marriage survey. Victorians are said to be "generally socially progressive, supportive of multiculturalism, wary of extremes of any kind".


title: Victoria (Australia)

text: Premier Daniel Andrews leads the Australian Labor Party that won the November 2014 Victorian state election.


title: Victoria (Australia)

text: The centre-left Australian Labor Party (ALP), the centre-right Liberal Party of Australia, the rural-based National Party of Australia, and the left-wing environmentalist Australian Greens are Victoria's main political parties. Traditionally, Labor is strongest in Melbourne's working and middle class western, northern and inner-city suburbs, and the regional cities of Ballarat, Bendigo and Geelong. The Liberals' main support lies in Melbourne's more affluent eastern suburbs and outer suburbs, and some rural and regional centres. The Nationals are strongest in Victoria's North Western and Eastern rural regional areas. The Greens, who won their first lower house seats in 2014, are strongest in inner Melbourne.


title: Victoria (Australia)

text: Victorian voters elect 50 representatives to the Parliament of Australia, including 38 members of the House of Representatives and 12 members of the Senate. Since 18 May 2019, the ALP has held 21 Victorian house seats, the Liberals 12, the Nationals three, the Greens one, and one held by an Independent. As of 1 July 2019, the Liberals have held five senate seats, the Nationals one, the ALP four, and the Greens two.


title: Victoria (Australia)

text: Victoria is incorporated into 79 municipalities for the purposes of local government, including 39 shires, 32 cities, seven rural cities and one borough. Shire and city councils are responsible for functions delegated by the Victorian parliament, such as city planning, road infrastructure and waste management. Council revenue comes mostly from property taxes and government grants.


title: Victoria (Australia)

text: Victoria's state school system dates back to 1872, when the colonial government legislated to make schooling both free and compulsory. The state's public secondary school system began in 1905. Before then, only private secondary schooling was available. Today, a Victorian school education consists of seven years of primary schooling (including one preparatory year) and six years of secondary schooling.


title: Victoria (Australia)

text: The final years of secondary school are optional for children aged over 17. Victorian children generally begin school at age five or six. On completing secondary school, students earn the Victorian Certificate of Education (VCE) or Victorian Certificate of Applied Learning (VCAL). Students who successfully complete their VCE also receive an ATAR, to determine university admittance.


title: Victoria (Australia)

text: Victorian schools are either publicly or privately funded. Public schools, also known as state or government schools, are funded and run directly by the Victoria Department of Education Department of Education and Training Victoria. Students do not pay tuition fees, but some extra costs are levied. Private fee-paying schools include parish schools run by the Roman Catholic Church and independent schools similar to British public schools. Independent schools are usually affiliated with Protestant churches. Victoria also has several private Jewish and Islamic primary and secondary schools. Private schools also receive some public funding. All schools must comply with government-set curriculum standards. In addition, Victoria has six government selective schools, Melbourne High School for boys, MacRobertson Girls' High School for girls, the coeducational schools John Monash Science School, Nossal High School and Suzanne Cory High School, and the Victorian College of the Arts Secondary School. Students at these schools are exclusively admitted on the basis of an academic selective entry test.


title: Victoria (Australia)

text: As of February 2019, Victoria had 1,529 public schools, 496 Catholic schools and 219 independent schools. Just under 631,500 students were enrolled in public schools, and just over 357,000 in private schools. Over 58 per cent of private students attend Catholic schools. More than 552,300 students were enrolled in primary schools and more than 418,600 in secondary schools. Retention rates for the final two years of secondary school were 84.3 per cent for public school students and 91.5 per cent for private school students. Victoria has about 46,523 full-time teachers.


title: Victoria (Australia)

text: Victoria has nine universities. The first to offer degrees, the University of Melbourne, enrolled its first student in 1855. The largest, Monash University, has an enrolment of over 83,000 students—more than any other Australian university.


title: Victoria (Australia)

text: The number of students enrolled in Victorian universities was 418,447 in 2018, an increase of 5.3% on the previous year. International students made up 40% of enrolments and account for the highest percentage of pre-paid university tuition fees. The largest number of enrolments were recorded in the fields of business, administration and economics, with nearly 30% of all students, followed by arts, humanities, and social science, with 18% of enrolments.


title: Victoria (Australia)

text: Victoria has 12 government-run institutions of technical and further education (TAFE). The first vocational institution in the state was the Melbourne Mechanics' Institute (established in 1839), which is now the Melbourne Athenaeum. More than 1,000 adult education organisations are registered to provide recognised TAFE programs. In 2014, there were 443,000 students enrolled in vocational education in the state. By 2018, the number of students in the sector had dropped by 40 per cent to 265,000—a five-year low which the education department attributed to withdrawal of funding to low-quality providers and a societal shift to university education.


title: Victoria (Australia)

text: The State Library Victoria is the State's research and reference library. It is responsible for collecting and preserving Victoria's documentary heritage and making it available through a range of services and programs. Material in the collection includes books, newspapers, magazines, journals, manuscripts, maps, pictures, objects, sound and video recordings and databases.


title: Victoria (Australia)

text: In addition, local governments maintain local lending libraries, typically with multiple branches in their respective municipal areas.


title: Victoria (Australia)

text: The state of Victoria is the second largest economy in Australia after New South Wales, accounting for a quarter of the nation's gross domestic product. The total gross state product (GSP) at current prices for Victoria was A$459 billion in June 2020, with a GSP per capita of A$68,996.


title: Victoria (Australia)

text: Finance and insurance is Victoria's largest income producing sector, while the health care and social assistance sector is the state's biggest employer. The shift towards service industries in the preceding decades has seen manufacturing lose its mantle as Victoria's largest employer and income producer.


title: Victoria (Australia)

text: During 2003–04, the gross value of Victorian agricultural production increased by 17% to $8.7 billion. This represented 24% of national agricultural production total gross value. As of 2004, an estimated 32,463 farms occupied around of Victorian land. This comprises more than 60% of the state's total land surface. Victorian farms range from small horticultural outfits to large-scale livestock and grain productions. A quarter of farmland is used to grow consumable crops.


title: Victoria (Australia)

text: More than of Victorian farmland are sown for grain, mostly in the state's west. More than 50% of this area is sown for wheat, 33% for barley and 7% for oats. A further is sown for hay. In 2003–04, Victorian farmers produced more than of wheat and of barley. "Pgt" standard race 126 was the most common ("Puccinia graminis" f. sp. "tritici") race here from 1929 to 1941, as it was for the whole of Australia. First detected on Tasmania in 1954, standard race 21 was the most common race by the next year in this state, the southern part of NSW, and Tasmania. ("P. triticina") is known to have been present here, and throughout the continent, at least since European colonization. "P. triticina" pathotype was first found here in 1984 and has contributed to populations ever since. It is considered to be foreign to Australia due to a difference in pathogenicity and due to its unique "" allele.


title: Victoria (Australia)

text: Victorian farms produce nearly 90% of Australian pears and a third of apples. It is also a leader in stone fruit ("Prunus") production. The main vegetable crops include asparagus, broccoli, carrots, potatoes and tomatoes. Last year, of pears and of tomatoes were produced.


title: Victoria (Australia)

text: More than 14 million sheep and 5 million lambs graze over 10% of Victorian farms, mostly in the state's north and west. In 2004, nearly 10 million lambs and sheep were slaughtered for local consumption and export. Victoria also exports live sheep to the Middle East for meat and to the rest of the world for breeding. More than of wool clip was also produced—one-fifth of the Australian total.


title: Victoria (Australia)

text: Victoria is the centre of dairy farming in Australia. It is home to 60% of Australia's 3 million dairy cattle and produces nearly two-thirds of the nation's milk, almost . The state also has 2.4 million beef cattle, with more than 2.2 million cattle and calves slaughtered each year. In 2003–04, Victorian commercial fishing crews and aquaculture industry produced of seafood valued at nearly A$109 million. Blacklipped abalone is the mainstay of the catch, bringing in A$46 million, followed by southern rock lobster worth A$13.7 million. Most abalone and rock lobster is exported to Asia.


title: Victoria (Australia)

text: Most of Australia including this state imposed a moratorium on GM canola in 2003 to consider the positives and negatives. After consideration the ban here was lifted in 2008 and the state's produced a review of the effects of the moratorium and the expected economic and other effects of adoption or failure to adopt GM canola. The government finds a benefit of AUS/season over conventional.


title: Victoria (Australia)

text: Victoria has a diverse range of manufacturing enterprises and Melbourne is considered Australia's most important industrial city. The post-World War II manufacturing boom was fuelled by international investment; attracted to the state by the availability of cheap land close to the city and inexpensive energy from the Latrobe Valley. Victoria produced 26.4% of total manufacturing output in Australia in 2015–16, behind New South Wales at 32.4%.


title: Victoria (Australia)

text: Machinery and equipment manufacturing is the state's most valuable manufacturing activity, followed by food and beverage products, petrochemicals and chemicals. Prominent manufacturing plants in the state include the Portland and Point Henry aluminium smelters, owned by Alcoa; Geelong and Altona oil refineries; a major petrochemical facility at Laverton; and Victorian-based CSL, a global biotechnology company that produces vaccines and plasma products, among others. Victoria also plays an important role in providing goods for the defence industry.


title: Victoria (Australia)

text: Victoria proportionally relies on manufacturing more than any other state in Australia, constituting 8.6% of total state product; slightly higher than South Australia at 8.0%. However, this proportion has been declining for three decades; in 1990 at the time of the early 1990s recession manufacturing constituted 20.3% of total state output. Manufacturing output peaked in absolute terms in 2008, reaching $28.8 billion and has slowly fallen over the decade to $26.8 billion in 2016 (−0.77% per annum). Since 1990, manufacturing employment has also fallen in both aggregate (367,700 to 274,400 workers) and proportional (17.8% to 9.0%) terms. The strong Australian dollar as a result of the 2000s mining boom, small population and isolation, high wage base and the general shift of manufacturing production towards developing countries have been cited as some of the reasons for this decline.


title: Victoria (Australia)

text: Historically, Victoria has been a hub for the manufacturing plants of the major car brands Ford, Toyota and Holden; however, closure announcements by all three companies in the 2010s has meant Australia will completely lose their car manufacturing industry by the end of 2017. Holden's announcement occurred in May 2013 following Ford's decision in December the previous year (Ford's Victorian plants, in Broadmeadows and Geelong, closed in October 2016). Toyota followed suit in February 2014 with an expected announcement as without Holden or Ford, local supply chains would struggle to create the economics of scale required to supply one manufacturer.


title: Victoria (Australia)

text: Victoria adopted the Torrens system of land registration with the "Real Property Act 1862". The Torrens system did not replace the common law system but applied only to new land grants and to land that has been voluntarily registered under the Act, and its successors. The common law system continues to apply to all other private landholdings. Crown land held in Victoria is managed under the "Crown Land (Reserves) Act 1978" and the "Land Act 1958".


title: Victoria (Australia)

text: Mining in Victoria contributes around A$6 billion to the gross state product (~2%) but employs less than 1% of workers. The Victorian mining industry is concentrated on energy producing minerals, with brown coal, petroleum and gas accounting for nearly 90% of local production. The oil and gas industries are centred off the coast of Gippsland in the state's east, while brown coal mining and power generation is based in the Latrobe Valley.


title: Victoria (Australia)

text: In the 2005–06 fiscal year, the average gas production was over per day (M cuft/d) and represented 18% of the total national gas sales, with demand growing at 2% per year.


title: Victoria (Australia)

text: In 1985, oil production from the offshore Gippsland Basin peaked to an annual average of per day. In 2005–2006, the average daily oil production has declined to /d, but despite the decline Victoria still produces almost 19.5% of crude oil in Australia.


title: Victoria (Australia)

text: Brown coal is Victoria's leading mineral, with 66 million tonnes mined each year for electricity generation in the Latrobe Valley, Gippsland. The region is home to the world's largest known reserves of brown coal.


title: Victoria (Australia)

text: Despite being the historic centre of Australia's gold rush, Victoria today contributes a mere 1% of national gold production. Victoria also produces limited amounts of gypsum and kaolin.


title: Victoria (Australia)

text: The service industries sector is the fastest growing component of the Victorian economy. It includes the wide range of activities generally classified as financial and professional services; health care and social assistance, education, transportation, IT and communication services, government services and wholesale and retail trade. Most service industries are located in Melbourne and the state's larger regional centres.


title: Victoria (Australia)

text: As of 2015–16, service industries employed over three-quarters of Victorian workers and more than three-quarters of the state's GSP. Finance and insurance as a group provide more value-add to the economy than any other economic activity in Victoria while health care and social assistance employ the most workers.


title: Victoria (Australia)

text: Major events that explore cultural diversity, music and sports play a big part in Victoria's tourism. The V8 Supercars and Australian Motorcycle Grand Prix at Phillip Island, the Grand Annual Steeplechase at Warrnambool and the Australian International Airshow at Avalon and numerous local festivals such as the popular Port Fairy Folk Festival, Queenscliff Music Festival, Pako Festa in Geelong West, Bells Beach Surf Classic and the Bright Autumn Festival amongst others.


title: Victoria (Australia)

text: Victoria has the highest population density in any state in Australia, with population centres spread out over most of the state; only the far northwest and the Victorian Alps lack permanent settlement.


title: Victoria (Australia)

text: The Victorian road network services the population centres, with highways generally radiating from Melbourne and other major cities and rural centres with secondary roads interconnecting the highways to each other. Many of the highways are built to freeway standard ("M" freeways), while most are generally sealed and of reasonable quality.


title: Victoria (Australia)

text: Rail transport in Victoria is provided by several private and public railway operators who operate over government-owned lines. Major operators include: Metro Trains Melbourne which runs an extensive, electrified, passenger system throughout Melbourne and suburbs; V/Line which is now owned by the Victorian Government, operates a concentrated service to major regional centres, as well as long-distance services on other lines; Pacific National, CFCL Australia which operate freight services; Great Southern Rail which operates "The Overland" Melbourne—Adelaide; and NSW TrainLink which operates XPTs Melbourne—Sydney.


title: Victoria (Australia)

text: There are also several smaller freight operators and numerous tourist railways operating over lines which were once parts of a state-owned system. Victorian lines mainly use the broad gauge. However, the interstate trunk routes, as well as a number of freight lines in the north and west of the state have been converted to standard gauge. Two tourist railways operate over narrow gauge lines, which are the remnants of five formerly government-owned lines which were built in mountainous areas.