Some quantum mechanical problems in Lobachevsky space

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