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Matematicheskie Zametki, 2012, Volume 92, Issue 4, Pages 583–596
DOI: https://doi.org/10.4213/mzm9067 (Mi mzm9067) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Asymptotics of the Spectrum and Quantum Averages near the Boundaries of Spectral Clusters for Perturbed Two-Dimensional Oscillators

A. V. Pereskokov

Moscow Power Engineering Institute (Technical University)
Full-text PDF (569 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm9067
Abstract: The eigenvalue problem for the perturbed resonant oscillator is considered. A method for constructing asymptotic solutions near the boundaries of spectral clusters using a new integral representation is proposed. The problem of calculating the averaged values of differential operators on solutions near the cluster boundaries is studied.
Keywords: spectral cluster, resonance, operator averaging method, coherent transform, WKB-approximation, turning point.
Received: 13.03.2011
English version:
Mathematical Notes, 2012, Volume 92, Issue 4, Pages 532–543
DOI: https://doi.org/10.1134/S0001434612090258
Bibliographic databases:
Document Type: Article
UDC: 517.958:530.145.6
Language: Russian
Citation: A. V. Pereskokov, “Asymptotics of the Spectrum and Quantum Averages near the Boundaries of Spectral Clusters for Perturbed Two-Dimensional Oscillators”, Mat. Zametki, 92:4 (2012), 583–596; Math. Notes, 92:4 (2012), 532–543
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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