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

DOI10.1134/S0040577919120079zbMath1441.81091OpenAlexW2997483338MaRDI QIDQ2190187

A. Yu. Anikin, S. Yu. Dobrokhotov, Vladimir E. Nazaikinskii, Anna V. Tsvetkova

Publication date: 18 June 2020

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577919120079

zbMATH Keywords

WKB approximationAiry functionbound statecanonical operatorclosed trajectorysemiclassical asymptotic solution

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

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Uses Software

• DLMF

Cites Work

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