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 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 cr; the degeneration multiplicity is computed for each eigenvalue.
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Original Russian Text © J. Brüning, R. V. Nekrasov, A. I. Shafarevich, 2007, published in Matematicheskie Zametki, 2007, Vol. 81, No. 1, pp. 32–42.
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Brüning, J., Nekrasov, R.V. & Shafarevich, A.I. Quantization of periodic motions on compact surfaces of constant negative curvature in a magnetic field. Math Notes 81, 28–36 (2007). https://doi.org/10.1134/S0001434607010038
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DOI: https://doi.org/10.1134/S0001434607010038