Particle with spin 1 in a magnetic field on the hyperbolic plane H_{2}

E. M. Ovsiyuk, O. V. Veko

Published 2011-10-12Version 1

There are constructed exact solutions of the quantum-mechanical equation for a spin S=1 particle in 2-dimensional Riemannian space of constant negative curvature, hyperbolic plane, in presence of an external magnetic field, analogue of the homogeneous magnetic field in the Minkowski space. A generalized formula for energy levels describing quantization of the motion of the vector particle in magnetic field on the 2-dimensional space H_{2} has been found, nonrelativistic and relativistic equations have been solved.