2014/10/30 by O. V. Veko, О. В. Веко, К. В. Казмерчук +12
Mathematics · Physics and Astronomy · #33E30 #34B30 #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #math-ph #math.MP #msc:33E30 #msc:34B30 #quant-ph
paper · pdf · doi:10.48550/arxiv.1410.8344
17 pages, Report to International Conference and Workshop "Quanta and %Matter: Through Physics to Future Emerging Technologies. 22-26 September 2014. Yerevan-Tsaghkadzor, Armenia
openalex publication_date 2014/10/30 · arxiv created 2014/12/28 · arxiv updated 2014/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.