This article is cited in 3 papers

Some quantum mechanical problems in Lobachevsky space

A. V. Shchepetilov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: For potentials, being the solutions of Bertrand's problem in Lobachevsky space, quantum mechanical problems are considered. The self-adjointness of the corresponding Schrödinger operators is proved. Energy levels are calculated both from Schrödinger equation and by the Bohr–Sommerfeld method. The effect of quantum binding of classical infinite states is discovered. It is shown that the semiclassical limit is equivalent in some sense to the Euclidean one.

Received: 19.02.1996

DOI: 10.4213/tmf1236

 English version: Theoretical and Mathematical Physics, 1996, 109:3, 1556–1564

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