Vol 3 - Landau, Lifshitz - Quantum mechanics - non-relativistic theory (3ed., 1991) · Problem 40.1

Perturbation Theory

Physics — Landau & Lifshitz · periodic-perturbation-near-resonance

Problem

Determine the change in the

n

th and

m

th solutions of Schrödinger's equation in the presence of a periodic perturbation (of the form (40.6)), of frequency

\omega

such that

E_m^{(0)} - E_n^{(0)} = \hbar(\omega + \epsilon)

, where

\epsilon

is a small quantity.