Phy5646/Non-degenerate Perturbation Theory - Problem 3

(Submitted by Team 1)

This example taken from "Quantum Physics" 3rd ed., Stephen Gasiorowicz, p. 177.

Problem: A charged particle in a simple harmonic oscillator, for which <math>{H}_0 = \frac{p^{2}}{2m} + \frac{mw^{2}}{2}</math, subject to a constant electric field so that H, = q%x. Calculate the energy shift for the nth level to first and second order in (q%). (Hint: Use the operators A and A+ for the evaluation of the matrix elements.)