Some quantum mechanical problems in Lobachevsky space

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.