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|Title:||Hydrogen Atom in de Sitter Spaces|
|Authors:||Veko, O. V.|
Dashuk, K. V.
Ovsiyuk, E. M.
Red’kov, V. M.
Ishkhanyan, A. M.
|Keywords:||ЭБ БГУ::ЕСТЕСТВЕННЫЕ И ТОЧНЫЕ НАУКИ::Физика|
|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.|
|ISSN:||1561 - 4085|
|Appears in Collections:||2016. Volume 19. Number 1|
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