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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2023, Number 5, Pages 22–32
DOI: https://doi.org/10.55959/MSU0579-9368-1-64-5-4 (Mi vmumm4564) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Spectrum of the Schrödinger operator in an elliptical ring cover

M. A. Nikulin

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (302 kB) Citations (1)
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DOI: https://doi.org/10.55959/MSU0579-9368-1-64-5-4
Abstract: The stationary Schrödinger equation is studied in a domain bounded by two confocal ellipses and in its coverings. The order of dependence of the Laplace operator eigenvalues on sufficiently small distance between the foci is obtained. Coefficients of the power series expansion of said eigenvalues are calculated up to and including the square of half the focal distance.
Key words: Mathieu funtions, stationary Schrödinger equation, Laplace operator spectrum, eigenvalue dependence on focal distance.
Funding agency Grant number
Russian Science Foundation 22-71-10106
Received: 18.01.2023
English version:
Moscow University Mathematics Bulletin, 2023, Volume 78, Issue 5, Pages 230–243
DOI: https://doi.org/10.3103/S0027132223050042
Bibliographic databases:
Document Type: Article
UDC: 517.984.5
Language: Russian
Citation: M. A. Nikulin, “Spectrum of the Schrödinger operator in an elliptical ring cover”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023, no. 5, 22–32; Moscow University Mathematics Bulletin, 78:5 (2023), 230–243
Citation in format AMSBIB
\Bibitem{Nik23}
\by M.~A.~Nikulin
\paper Spectrum of the Schr\"odinger operator in an elliptical ring cover
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2023
\issue 5
\pages 22--32
\mathnet{http://mi.mathnet.ru/vmumm4564}
\crossref{https://doi.org/10.55959/MSU0579-9368-1-64-5-4}
\elib{https://elibrary.ru/item.asp?id=54669689}
\transl
\jour Moscow University Mathematics Bulletin
\yr 2023
\vol 78
\issue 5
\pages 230--243
\crossref{https://doi.org/10.3103/S0027132223050042}
Linking options:
  • https://www.mathnet.ru/eng/vmumm4564
  • https://www.mathnet.ru/eng/vmumm/y2023/i5/p22
    • This publication is cited in the following 1 articles:
    1. M. A. Nikulin, Th. Yu. Popelensky, A. I. Shafarevich, “Asymptotic behaviour of energy levels of a quantum free particle in an elliptic sector”, Phys. Scr., 99:1 (2024), 015207  mathnet  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:130
    Full-text PDF :72
    References:27
     
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