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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 205, Number 3, Pages 467–483
DOI: https://doi.org/10.4213/tmf9934 (Mi tmf9934) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

A. V. Pereskokovab

a National Research University "Higher School of Economics", Moscow, Russia
b National Research University "Moscow Power Engineering Institute", Moscow, Russia
Full-text PDF (463 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf9934
Abstract: We consider the eigenvalue problem for the two-dimensional Hartree operator with a small nonlinearity coefficient. We find the asymptotic eigenvalues and asymptotic eigenfunctions near a local maximum of the eigenvalues in spectral clusters formed near the eigenvalues of the unperturbed operator.
Keywords: spectral cluster, WKB approximation, asymptotic eigenvalue, asymptotic eigenfunction, logarithmic singularity.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FSWF-2020-0022
This research was performed in the framework of a state task of the Ministry of Education and Science of the Russian Federation (Project No. FSWF-2020-0022).
Received: 13.05.2020
Revised: 31.07.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 205, Issue 3, Pages 1652–1665
DOI: https://doi.org/10.1134/S0040577920120077
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Pereskokov, “Semiclassical asymptotic spectrum of the two-dimensional Hartree operator near a local maximum of the eigenvalues in a spectral cluste”, TMF, 205:3 (2020), 467–483; Theoret. and Math. Phys., 205:3 (2020), 1652–1665
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf9934
  • https://doi.org/10.4213/tmf9934
  • https://www.mathnet.ru/eng/tmf/v205/i3/p467
    • This publication is cited in the following 2 articles:
    1. A. V. Pereskokov, “Asymptotics of the Spectrum of a Hartree Type Operator with Self-Consistent Potential Including the Macdonald Function”, J Math Sci, 279:4 (2024), 508  crossref  mathscinet
    2. E. V. Vybornyi, S. V. Rumyantseva, “Semiclassical Asymptotics of Oscillating Tunneling for a Quadratic Hamiltonian on the Algebra su(1,1)su(1,1)”, Math. Notes, 112:5 (2022), 642–655  mathnet  crossref  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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