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

Dimitri R Yafaev (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

The semiclassical limit, as the Planck constant (h) over bar tends to 0, of bound states of a quantum particle in a one-dimensional potential well is considered. The semiclassical asymptotic formulas for eigenfunctions are justified, and the Bohr-Sommerfeld quantization condition is recovered.

Keywords: Schrodinger equation; potential well; Airy functions; Green-Liouville approximation; Bohr-Sommerfeld quantization condition; semiclassical Weyl formula

Domains: Analysis of PDEs [math.AP]

Dimitri R Yafaev. The semiclassical limit of eigenfunctions of the Schrödinger equation and the Bohr-Sommerfeld quantization condition, revisited. St. Petersburg Mathematical Journal, 2011, 22 (6), pp.1051-1067. ⟨10.1090/S1061-0022-2011-01183-5⟩. ⟨hal-00671997⟩