Nonlinear Phenomena in Complex Systems, 2012, Vol.15, No.1, pp.43-57

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2012, Vol.15, No.1, pp.43-57

On a Dirac Particle in a Uniform Magnetic field in 3-Dimensional Space of Constant Negative Curvature.
E. M. Ovsiyuk, V. V. Kisel, and V. M. Red'kov

There are constructed exact solutions of the quantum-mecha\-nical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature,hyperbolic Lobachevsky space, 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 trans\-versal motion of the particle in magnetic field has been obtained.

Key words: Spaces of constant curvature, magnetic field, separation of variables, Dirac equation, bound states

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