What is seen in an electron diffraction pattern depends upon the sample and also the energy of the electrons. The electrons need to be considered as waves, which involves describing the electron via a wavefunction, written in crystallographic notation (see notes and) as: ψ ψ ( r ) = exp ⁡ ⁡ ( 2 π π i k ⋅ ⋅ r ) for a position r . This is a quantum mechanics description; one cannot use a classical approach. The vector k is called the wavevector, has units of inverse nanometers, and the form above is called a plane wave as the term inside the exponential is constant on the surface of a plane. The vector k is what is used when drawing ray diagrams, and in vacuum is parallel to the direction or, better, group velocity or probability current of the plane wave. For most cases the electrons are travelling at a respectable fraction of the speed of light, so rigorously need to be considered using relativistic quantum mechanics via the Dirac equation, which as spin does not normally matter can be reduced to the Klein–Gordon equation. Fortunately one can side-step many complications and use a non-relativistic approach based around the Schrödinger equation. Following Kunio Fujiwara and Archibald Howie, the relationship between the total energy of the electrons and the wavevector is written as: E = h 2 k 2 2 m ∗ ∗ with m ∗ ∗ = m 0 + E 2 c 2 where h is Planck's constant, m ∗ ∗ is a relativistic effective mass used to cancel out the relativistic terms for electrons of energy E with c the speed of light and m 0 the rest mass of the electron. The concept of effective mass occurs throughout physics (see for instance Ashcroft and Mermin), and comes up in the behavior of quasiparticles. A common one is the electron hole, which acts as if it is a particle with a positive charge and a mass similar to that of an electron, although it can be several times lighter or heavier. For electron diffraction the electrons behave as if they are non-relativistic particles of mass m ∗ ∗ in terms of how they interact with the atoms.