Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems

A. Yu. Anikin ; S. Yu. Dobrokhotov ; V. E. Nazaikinskii ; A. V. Tsvetkova

Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 3, pp. 382-414

Résumé

We consider stationary scalar and vector problems for differential and pseudodifferential operators leading to the appearance of asymptotic solutions of one-dimensional problems localized in a neighborhood of intervals (“bound states”). Based on the semiclassical approximation and the Maslov canonical operator, we develop a constructive algorithm that allows writing an asymptotic solution globally under certain conditions using an Airy function of complex argument.

Détail

Keywords: semiclassical asymptotic solution, bound state, closed trajectory, WKB approximation, canonical operator, Airy function.

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