Nonlinear Phenomena in Complex Systems, 2008, Vol.11, No.4, pp.403-416

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2008, Vol.11, No.4, pp.403-416

Schrödinger Particle in Magnetic and Electric Fields in Lobachevsky and Riemann Spaces.
A. A. Bogush, V. M. Red'kov, and G. G. Krylov

Schrödinger equation in Lobachevsky and Riemann 4-spaces has been solved in the presence of external magnetic field that is an analog of a uniform magnetic field in the flat space. Generalized Landau levels have been found, modified by the presence of the space curvature. In Lobachevsky 4-model the energy spectrum contains discrete and continuous parts, the number of bound states is finite; in Riemann 4-model all energy spectrum is discrete. Generalized Landau levels are determined by three parameters, the magnitude of the magnetic field B, the curvature radius and the magnetic quantum number m. It has been shown that in presence of an additional external electric field the energy spectrum in the Riemann model can be also obtained analytically.
Key words: magnetic field, Landau system, Schrödinger equation, hyperbolical 3-space, spherical 3-space, energy levels

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