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arXiv · 1007.4253

On a Dirac particle in an uniform magnetic field in 3-dimensional spaces of constant curvature

E. M. Ovsiyuk·V. V. Kisel·V. M. Red'kov
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Abstract

There are constructed exact solutions of the quantum-mechanical 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 transversal motion of the particle in magnetic field has been obtained. The same problem is solved for spin 1/2 particle in the space of constant positive curvature, spherical Riemann space. A generalized formula for energy levels, describing quantization of the transversal and along the magnetic field motions of the particle on the background of the Riemann space geometry, is obtained.

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E. M. Ovsiyuk, V. V. Kisel, V. M. Red'kov. 2010-07-24. On a Dirac particle in an uniform magnetic field in 3-dimensional spaces of constant curvature. https://arxiv.org/abs/1007.4253

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