Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters

DOI10.1134/S0040577916040061zbMath1342.81136MaRDI QIDQ2628897

A. V. Pereskokov

Publication date: 19 July 2016

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

zbMATH Keywords

logarithmic singularityself-consistent fieldspectral clusterasymptotic eigenvalueasymptotic eigenfunction

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) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20)

Related Items (8)

Semiclassical asymptotics of the spectrum of a two-dimensional Hartree type operator near boundaries of spectral clusters ⋮ Asymptotics of the spectrum of a Hartree-type operator with a screened Coulomb self-action potential near the upper boundaries of spectral clusters ⋮ Semiclassical asymptotics of solutions to Hartree type equations concentrated on segments ⋮ Asymptotics of the spectrum of a two-dimensional Hartree type operator near upper boundaries of spectral clusters. Asymptotic solutions located near a circle ⋮ Asymptotic solutions to the Hartree equation near a sphere. Asymptotics of self-consistent potentials ⋮ Asymptotics of the spectrum and quantum averages of a Hartree type operator near the lower boundaries of spectral clusters ⋮ Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluster ⋮ Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters

Cites Work

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