A Modern Approach to Quantum Mechanics · Problem 11.3

Identical Particles — John S. Townsend

Physics — Quantum Mechanics · harmonic-oscillator-frequency-perturbation

Problem

For the simple harmonic oscillator, for which H^0=p^x22m+12mω2x^2\hat{H}_0 = \frac{\hat{p}_x^2}{2m} + \frac{1}{2}m\omega^2\hat{x}^2 take the perturbing Hamiltonian to be H^1=12mω12x^2\hat{H}_1 = \frac{1}{2}m\omega_1^2\hat{x}^2 where ω1≪ω\omega_1 \ll \omega. Calculate the energy shifts through second order and compare with the exact eigenvalues.

Related theory

Browse the problem library