Schr\'{o}dinger particle in magnetic and electric fields in Lobachevsky and Riemann spaces
| Autor: | Bogush, A. A., Red'kov, V. M., Krylov, G. G. |
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| Rok vydání: | 2010 |
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| Zdroj: | Nonlinear Phenomena in Complex Systems. 2008. Vol. 11, P. 403 -- 416 |
| Druh dokumentu: | Working Paper |
| Popis: | Schr\"{o}dinger 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 Lobachevsky4-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 $\rho$ 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. Comment: 18 pages |
| Databáze: | arXiv |
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