Hydrogen atom in de Sitter spaces

zbMATH Open1353.81129arXiv1410.8344MaRDI QIDQ2951861

Olga V. Veko, K. V. Dashuk, A. M. Ishkhanyan, Elena M. Ovsiyuk, Viktor M. Red'kov

Publication date: 10 January 2017

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.

Full work available at URL: https://arxiv.org/abs/1410.8344

zbMATH Keywords

hydrogen atomquantum mechanicsde Sitter spaceanti de Sitter spacegeneral Heun functionsWKB-approach

Mathematics Subject Classification ID

Atomic physics (81V45) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Related Items (3)

A confined hydrogen atom in higher space dimensions ⋮ Hydrogen atom and its energy level shifts in de Sitter universe ⋮ On the existence of hydrogen atoms in higher dimensional Euclidean spaces

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