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

The semiclassical limit, as the Planck constant $\hbar$ tends to 0, of bound states of a quantum particle in a one-dimensional potential well is considered. The semiclassical asymptotics of eigenfunctions is justified, and the Bohr–Sommerfeld quantization condition is recovered.