On exact solutions of the Dirac equation in a homogeneous magnetic field in the Lobachevsky space

摘要

There are constructed exact solutions of the quantum-mechanical Diracequation for a spin S=1/2 particle in Riemannian space of constant negativecurvature, hyperbolic Lobachevsky space, in presence of an external magneticfield, analogue of the homogeneous magnetic field in the Minkowski space. Ageneralized formula for energy levels, describing quantization of the motion ofthe particle in magnetic field on the background of the Lobachevsky spacegeometry, has been obtained.