Abstract
Quantum mechanical problems are considered for potentials satisfying Bertrand's problem in Lobachevsky space. The self-adjointness of the corresponding Schrodinger operators is proved. The energy levels are calculated both from the Schrodinger 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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