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Matematicheskie Zametki, 2007, Volume 81, Issue 1, Pages 32–42
DOI: https://doi.org/10.4213/mzm3515
(Mi mzm3515)
 

This article is cited in 6 scientific papers (total in 6 papers)

Quantization of Periodic Motions on Compact Surfaces of Constant Negative Curvature in a Magnetic Field

J. Brüninga, R. V. Nekrasova, A. I. Shafarevichb

a M. V. Lomonosov Moscow State University
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (510 kB) Citations (6)
References:
Abstract: We use the semiclassical approach to study the spectral problem for the Schrödinger operator of a charged particle confined to a two-dimensional compact surface of constant negative curvature. We classify modes of classical motion in the integrable domain $E<E_{\textup{cr}}$ and obtain a classification of semiclassical solutions as a consequence. We construct a spectral series (spectrum part approximated by semiclassical eigenvalues) corresponding to energies not exceeding the threshold value $E_{\textup{cr}}$; the degeneration multiplicity is computed for each eigenvalue.
Keywords: Schrödinger equation, eigenvalue asymptotics, semiclassical approximation, confined classical motion, surface of negative curvature, symplectic structure.
Received: 17.05.2006
Revised: 28.06.2006
English version:
Mathematical Notes, 2007, Volume 81, Issue 1, Pages 28–36
DOI: https://doi.org/10.1134/S0001434607010038
Bibliographic databases:
UDC: 517.958+530.145.6
Language: Russian
Citation: J. Brüning, R. V. Nekrasov, A. I. Shafarevich, “Quantization of Periodic Motions on Compact Surfaces of Constant Negative Curvature in a Magnetic Field”, Mat. Zametki, 81:1 (2007), 32–42; Math. Notes, 81:1 (2007), 28–36
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm3515
  • https://www.mathnet.ru/eng/mzm/v81/i1/p32
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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