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

2010/09/07 by Yafaev, D. R. · 2 citations
#47A40 #81U05 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1009.1378

Abstract

Consider the semiclassical limit, as the Planck constant ℏ\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.

Cited by

• Bohr-Sommerfeld Quantization Rules for 1-D Semiclassical Pseudo-Differential Operator: the Method of Microlocal Wronskian and Gram Matrix
• Cauchy Data for 1D singular Schrödinger operators

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