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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 178, Number 1, Pages 88–106
DOI: https://doi.org/10.4213/tmf8561 (Mi tmf8561) 		 
This article is cited in 12 scientific papers (total in 12 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
Full-text PDF (549 kB) Citations (12)
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DOI: https://doi.org/10.4213/tmf8561
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.
Received: 09.06.2013
English version:
Theoretical and Mathematical Physics, 2014, Volume 178, Issue 1, Pages 76–92
DOI: https://doi.org/10.1007/s11232-014-0131-8
Bibliographic databases:
Document Type: Article
Language: Russian
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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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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