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TMF, 2014, Volume 178, Number 1, Pages 88–106 (Mi tmf8561)  

This article is cited in 5 scientific papers (total in 5 papers)

Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters

A. V. Pereskokovab

a Moscow Power Engineering Institute, Moscow, Russia
b Moscow Institute for Electronics and Mathematics, Higher School of Economics, Moscow, Russia

Abstract: We consider the problem for eigenvalues of a perturbed two-dimensional oscillator in the case of a resonance frequency. The exciting potential is given by a Hartree-type integral operator with a smooth self-action potential. We find asymptotic eigenvalues and asymptotic eigenfunctions near the upper boundary of spectral clusters, which form around energy levels of the nonperturbed operator. To calculate them, we use asymptotic formulas for quantum means.

Keywords: self-consistent field, method of quantum averaging, coherent transformation, WKB approximation, spectral cluster, quantum mean

DOI: https://doi.org/10.4213/tmf8561

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English version:
Theoretical and Mathematical Physics, 2014, 178:1, 76–92

Bibliographic databases:

Received: 09.06.2013

Citation: A. V. Pereskokov, “Semiclassical asymptotic spectrum of a Hartree-type operator near the upper boundary of spectral clusters”, TMF, 178:1 (2014), 88–106; Theoret. and Math. Phys., 178:1 (2014), 76–92

Citation in format AMSBIB
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  • https://doi.org/10.4213/tmf8561
  • http://mi.mathnet.ru/eng/tmf/v178/i1/p88

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Pereskokov, “Asymptotics of the Hartree operator spectrum near the upper boundaries of spectral clusters: Asymptotic solutions localized near a circle”, Theoret. and Math. Phys., 183:1 (2015), 516–526  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. V. Pereskokov, “Semiclassical asymptotic approximation of the two-dimensional Hartree operator spectrum near the upper boundaries of spectral clusters”, Theoret. and Math. Phys., 187:1 (2016), 511–524  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Pereskokov A., “Asymptotics of the Hartree-type operator spectrum near the lower boundaries of spectral clusters”, Appl. Anal., 95:7, SI (2016), 1560–1569  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. V. Pereskokov, “Semiclassical Asymptotics of the Spectrum near the Lower Boundary of Spectral Clusters for a Hartree-Type Operator”, Math. Notes, 101:6 (2017), 1009–1022  mathnet  crossref  crossref  mathscinet  isi  elib
    5. D. A. Vakhrameeva, A. V. Pereskokov, “Asymptotics of the spectrum of a two-dimensional Hartree-type operator with a Coulomb self-action potential near the lower boundaries of spectral clusters”, Theoret. and Math. Phys., 199:3 (2019), 864–877  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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