Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluster

DOI10.1134/S0040577920120077zbMath1458.81022OpenAlexW3113430117MaRDI QIDQ2229347

A. V. Pereskokov

Publication date: 23 February 2021

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

Full work available at URL: https://doi.org/10.1134/s0040577920120077

zbMATH Keywords

WKB approximationlogarithmic singularityspectral clusterasymptotic eigenvalueasymptotic eigenfunction

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic expansions of solutions to PDEs (35C20) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Perturbation theories for operators and differential equations in quantum theory (81Q15) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (1)

Semiclassical asymptotics of oscillating tunneling for a quadratic Hamiltonian on the algebra \(\operatorname{su}(1,1)\)

Cites Work

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• Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters
• Algebras with general commutation relations and their applications. II. Unitary-nonlinear operator equations
• Asymptotics of the spectrum of a two-dimensional Hartree type operator near upper boundaries of spectral clusters. Asymptotic solutions located near a circle
• Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters
• Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: asymptotic solutions localized near a circle
• Semiclassical asymptotics of the spectrum near the lower boundary of spectral clusters for a Hartree-type operator
• Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters
• Solitons in Molecular Systems

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