Vol 3 - Landau, Lifshitz - Quantum mechanics - non-relativistic theory (3ed., 1991) · Problem 38.3

Perturbation Theory

Physics — Landau & Lifshitz · anharmonic-oscillator-energy-levels

Problem

Determine the energy levels of an anharmonic linear oscillator whose Hamiltonian is

\hat{H} = \tfrac{1}{2}\hat{p}^2/m + \tfrac{1}{2}m x^2 \omega^2 + \alpha x^3 + \beta x^4.