Vol 3 - Landau, Lifshitz - Quantum mechanics - non-relativistic theory (3ed., 1991) · Problem 4

Motion in a Centrally Symmetric Field

Physics — Landau & Lifshitz · three-dimensional-harmonic-oscillator

Problem

Determine the energy levels of a three-dimensional oscillator (a particle in a field

U = \frac{1}{2}m\omega^2 r^2

), their degrees of degeneracy, and the possible values of the orbital angular momentum in the corresponding stationary states.