Geodesic
Quantization of Periodic Motions on Compact Surfaces of Constant Negative Curvature in a Magnetic Field
Matematičeskie zametki, Tome 81 (2007) no. 1, pp. 32-42.

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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 $E$ 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. 
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J. Brüning; R. V. Nekrasov; A. I. Shafarevich. Quantization of Periodic Motions on Compact Surfaces of Constant Negative Curvature in a Magnetic Field. Matematičeskie zametki, Tome 81 (2007) no. 1, pp. 32-42. http://geodesic.mathdoc.fr/item/MZM_2007_81_1_a2/

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