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Please use this identifier to cite or link to this item: http://elib.bsu.by/handle/123456789/170480
Title: Hydrogen Atom in de Sitter Spaces
Authors: Veko, O. V.
Dashuk, K. V.
Ovsiyuk, E. M.
Red’kov, V. M.
Ishkhanyan, A. M.
Issue Date: 2016
Publisher: Minsk : Education and Upbringing
Citation: Nonlinear Phenomena in Complex Systems. - 2016. - Vol. 19, N 1. - P. 16-29
Abstract: The hydrogen atom theory is developed for the de Sitter and anti de Sitter spaces of constant negative curvature on the basis of the Klein-Gordon-Fock wave equation in static coordinates. In both models, after separation of variables, the problem is reduced to the general Heun equation, a second order linear differential equation having four regular singular points. Qualitative examination shows that the energy spectrum for the hydrogen atom in the de Sitter space should be quasi-stationary, and the atom should be unstable. We derive an approximate expression for energy levels within the quasi-classical approach and estimate the probability of decay of the atom. A similar analysis shows that in the anti de Sitter model the hydrogen atom should be stable in the quantum-mechanical sense. Using the quasi-classical approach, we derive approximate formulas for the energy levels for this case as well. Finally, we present the extension to the case of a spin 1/2 particle for both de Sitter models. This extension leads to complicated differential equations with 8 singular points.
URI: http://elib.bsu.by/handle/123456789/170480
ISSN: 1561 - 4085
Appears in Collections:2016. Volume 19. Number 1

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