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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm3515https://doi.org/10.4213/mzm3515 https://www.mathnet.ru/eng/mzm/v81/i1/p32
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Abstract page: | 485 | Full-text PDF : | 237 | References: | 77 | First page: | 5 |
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