Phy5646/Simpe Example of Time Dep Pert

This example taken from "Quantum Physics" 3rd ed., Stephen Gasiorowicz, p. 237-238.

Problem: A particle of charge $q$ in a one-dimensional harmonic oscillator of characteristic frequency $\omega$ is placed in an electric field that is turned on and off so that the potential energy is

$\lambda V(t)$