Asymptotics of wave functions of the stationary Schrödinger equation in the Weyl chamber

DOI10.1134/S0040577918110065zbMath1411.81090OpenAlexW2903681133MaRDI QIDQ1735001

S. Yu. Dobrokhotov, D. S. Minenkov, Senya B. Shlosman

Publication date: 27 March 2019

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

Full work available at URL: https://doi.org/10.1134/s0040577918110065

zbMATH Keywords

spectrumboundary value problemAiry functionquantization conditionstationary Schrödinger equationMaslov canonical operatorWeyl-Chamber-type polyhedral angle

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Lagrangian submanifolds; Maslov index (53D12) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (8)

Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems ⋮ Asymptotics of the whispering gallery-type in the eigenproblem for the Laplacian in a domain of revolution diffeomorphic to a solid torus ⋮ Efficient formulas for the Maslov canonical operator near a simple caustic ⋮ Tightness and Line Ensembles for Brownian Polymers Under Geometric Area Tilts ⋮ Lagrangian manifolds related to the asymptotics of Hermite polynomials ⋮ Asymptotic eigenfunctions of the ``bouncing ball type for the two-dimensional Schrödinger operator with a symmetric potential ⋮ An approach to finding the asymptotics of polynomials given by recurrence relations ⋮ Classical and quantum dynamics of a particle in a narrow angle

Cites Work

• Dyson Ferrari-Spohn diffusions and ordered walks under area tilts
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• An invariance principle to Ferrari-Spohn diffusions
• Bohr-Sommerfeld rules to all orders
• Statistical properties of the spectra of Laplace-Beltrami operators on Liouville surfaces
• Uniform approximation for potential scattering involving a rainbow
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