New problems in quantum mechanics and the Heun equation

Theoretical physics
Authors:
Veko Olga V. Kisel Vasiliy V. Red'kov Victor M. Ovsiyuk Elena M.
Abstract:

The system of equations for electromagnetic field in the Lobachevsky space is transformed into a single equation which formally coincides with an 1-dimensional Schrodinger equation with an effective potential; on this base, analysis of ideal mirror properties of the medium sumulated by the Lobachevsky geometry is performed. The problem of a spin 1 particle in the Coulomb field is reduced to the Heun equation and to a special class of the Heun functions.