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arXiv · 1410.8344

Hydrogen atom in de Sitter spaces

O. V. Veko·K. V. Kazmerchuk·E. M. Ovsiyuk·V. M. Red'kov·A. M. Ishkhanyan
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Abstract

The hydrogen atom theory is developed for the de Sitter and anti de Sitter spaces on the basis of the Klein-Gordon-Fock wave equation in static coordinates. In both models, after separation of the variables, the problem is reduced to the general Heun equation, a second order linear differential equation having four regular singular points. A 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 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.

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O. V. Veko, K. V. Kazmerchuk, E. M. Ovsiyuk, V. M. Red'kov, A. M. Ishkhanyan. 2014-12-28. Hydrogen atom in de Sitter spaces. https://arxiv.org/abs/1410.8344

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