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Izvestiya: Mathematics, 2013, Volume 77, Issue 1, Pages 163–210
DOI: https://doi.org/10.1070/IM2013v077n01ABEH002632 (Mi im7805) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters

A. V. Pereskokov

Moscow Power Engineering Institute (Technical University)
English version PDF (634 kB) Citations (10)
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DOI: https://doi.org/10.1070/IM2013v077n01ABEH002632
Abstract: In the eigenvalue problem for a perturbed two-dimensional oscillator, we suggest a method for constructing asymptotic solutions near the boundaries of spectral clusters by means of a new integral representation and study the issue of calculating the average values of differential operators on the solutions near the boundaries of the clusters.
Keywords: operator averaging method, coherent transform, WKB-approximation, turning point, spectral cluster.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00627-а
Ministry of Education and Science of the Russian Federation 14.В37.21.0864
НШ-3439.2010.1
Received: 04.07.2011
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2013, Volume 77, Issue 1, Pages 165–210
DOI: https://doi.org/10.4213/im7805
Bibliographic databases:
Document Type: Article
UDC: 517.984+517.958
MSC: 35P20, 35Q40, 47N50, 81Q20
Language: English
Original paper language: Russian
Citation: A. V. Pereskokov, “Asymptotics of the spectrum and quantum averages of a perturbed resonant oscillator near the boundaries of spectral clusters”, Izv. RAN. Ser. Mat., 77:1 (2013), 165–210; Izv. Math., 77:1 (2013), 163–210
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM2013v077n01ABEH002632
  • https://www.mathnet.ru/eng/im/v77/i1/p165
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:692
    Russian version PDF:215
    English version PDF:14
    References:111
    First page:31
     
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