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Some quantum mechanical problems in Lobachevsky space

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Abstract

Quantum mechanical problems are considered for potentials satisfying Bertrand's problem in Lobachevsky space. The self-adjointness of the corresponding Schrödinger operators is proved. The energy levels are calculated both from the Schrödinger equation and by means of the Bohr-Sommerfeld method. The effect of the quantum binding of classically infinite motion was discovered and is presented for the first time. It is shown that the quasi-classical limit is equivalent, in a sense, to the Euclidean limit.

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Authors and Affiliations

  1. Moscow State University, USSR

    A. V. Shchepetilov

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  1. A. V. Shchepetilov
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 395–405, December, 1996.

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Shchepetilov, A.V. Some quantum mechanical problems in Lobachevsky space. Theor Math Phys 109, 1556–1564 (1996). https://doi.org/10.1007/BF02073872

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  • DOI: https://doi.org/10.1007/BF02073872

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