A Modern Approach to Quantum Mechanics · Problem 11.11

Identical Particles — John S. Townsend

Physics — Quantum Mechanics · two-dimensional-harmonic-oscillator-perturbation

Problem

For the two-dimensional harmonic oscillator, the unperturbed Hamiltonian is given by

\hat{H}_0 = \frac{\hat{p}_x^2}{2m} + \frac{1}{2}m\omega^2\hat{x}^2 + \frac{\hat{p}_y^2}{2m} + \frac{1}{2}m\omega^2\hat{y}^2

Determine the first-order energy shifts to the ground state and the degenerate first excited states due to the perturbation

\hat{H}_1 = b\hat{x}\hat{y}