Uniform asymptotics in the form of Airy functions for bound states of the quantum anisotropic Kepler problem localized in a neighborhood of annuli

DOI10.1134/S1061920822010058zbMath1487.81093OpenAlexW4293097275MaRDI QIDQ2120148

A. I. Klevin

Publication date: 31 March 2022

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1061920822010058

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Two-body problems (70F05) Atomic physics (81V45) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Orbital mechanics (70M20)

Related Items (1)

New integral representations for the Maslov canonical operator on an isotropic manifold with a complex germ

Cites Work

• Chaos in classical and quantum mechanics
• Methods of noncommutative analysis: theory and applications
• Efficient formulas for the Maslov canonical operator near a simple caustic
• Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems
• Asymptotic eigenfunctions of the ``bouncing ball type for the two-dimensional Schrödinger operator with a symmetric potential
• New integral representations of the Maslov canonical operator in singular charts
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