Semiclassical asymptotics of the spectrum near the lower boundary of spectral clusters for a Hartree-type operator

DOI10.1134/S0001434617050285zbMath1371.81116OpenAlexW2657160813MaRDI QIDQ2401667

A. V. Pereskokov

Publication date: 4 September 2017

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434617050285

zbMATH Keywords

WKB approximationturning pointself-consistent fieldcoherent transformationspectral clusterquantum averaging method

Mathematics Subject Classification ID

General spectral theory of ordinary differential operators (34L05) NLS equations (nonlinear Schrödinger equations) (35Q55) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Boundary value problems on infinite intervals for ordinary differential equations (34B40)

Related Items (5)

Semiclassical asymptotics of the spectrum of a two-dimensional Hartree type operator near boundaries of spectral clusters ⋮ Semiclassical asymptotics of solutions to Hartree type equations concentrated on segments ⋮ 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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• Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters
• Asymptotics of eigenvalue clusters for the Laplacian plus a potential
• Asymptotics of the spectrum and quantum averages near the boundaries of spectral clusters for perturbed two-dimensional oscillators
• Semiclassical spectral series of a Hartree-type operator corresponding to a rest point of the classical Hamilton-ehrenfest system
• Asymptotic and geometric quantization
• Asymptotic solutions of Hartree equations concentrated near low-dimensional submanifolds. II. Localization in planar discs
• Asymptotic solutions of Hartree equations concentrated near low-dimensional submanifolds. I. The model with logarithmic singularity
• Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters

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