The semiclassical limit of eigenfunctions of the Schrödinger equation and the Bohr–Sommerfeld quantization condition, revisited

Abstract

Consider the semiclassical limit, as the Planck constant $\hbar\ri 0$, of bound states of a quantum particle in a one-dimensional potential well. We justify the semiclassical asymptotics of eigenfunctions and recover the Bohr-Sommerfeld quantization condition.