Equations to describe quantum systems can be seen as equivalent to that of classical dynamics on a macroscopic scale, except for the important detail that the variables don't follow the commutative laws of multiplication. Hence, as a fundamental principle, these variables are instead described as " q-numbers ", conventionally represented by operators or Hermitian matrices on a Hilbert space. Indeed, the state of the system in the atomic and subatomic scale is described not by dynamic variables with specific numerical values, but by state functions that are dependent on the c-number time. In this realm of quantum systems, the equation of motion governing dynamics heavily relies on the Hamiltonian, also known as the total energy. Therefore, to anticipate the time evolution of the system, one only needs to determine the initial condition of the state function |Ψ(t) and its first derivative with respect to time.