Transition of state

In quantum mechanics, particularly Perturbation theory, a transition of state is a change from an initial quantum state to a final one.

The following treatment is fairly common in literature (though here its slightly adapted), and often referred as time-dependent perturbation theory in a more advanced form.

We assume a one-dimensional quantum harmonic oscillator of mass m and charge e. The expression for the potential energy of this system is this of the harmonic oscillator.

The total wavefunction is denoted by Ψ(x, t) (capital Psi), and the spatial part of the wave function is ψ(x) (lower case psi). As we deal with stationary states, the total wave function is a solution of the Schrödinger equation and reads

with eigenvalue ${\displaystyle \textstyle i\hbar {\frac {\partial \Psi }{\partial t}}=E\Psi }$.

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