Hydrogen atom in de Sitter spaces
| Autor: | Veko, O. V., Kazmerchuk, K. V., Ovsiyuk, E. M., Red'kov, V. M., Ishkhanyan, A. M. |
|---|---|
| Rok vydání: | 2014 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 17 pages, Report to International Conference and Workshop "Quanta and %Matter: Through Physics to Future Emerging Technologies. 22-26 September 2014. Yerevan-Tsaghkadzor, Armenia |
| Databáze: | arXiv |
| Externí odkaz: |
|