Dirac particle in the external coulomb field on the background of the Lobachevsky–Riemann space models
https://doi.org/10.29235/1561-8323-2021-65-2-146-157
Abstract
The known systems of the radial equations describing the hydrogen atom on the basis of the Dirac equation in the Lobachevsky–Riemann spaces of constant curvature are investigated. In the both geometrical models, the differential equations of second order with six regular singular points are found, and their exact solutions of Frobenius type are constructed. To produce the quantization rule for energy values we use the known condition which separates the transcendental Frobenius solutions. This provides us with the energy spectra that are physically interpretable and are similar to those for the Klein–Fock–Gordon particle in these space models. These spectra are similar to those that previously have appeared in studying the same systems of the equations with the use of the semi-classical approximation.
About the Authors
E. M. Оvsiyuk
Mozyr State Pedagogical University named after I. P. Shamyakin
Belarus
Belarus
Оvsiyuk Еlena М., Ph. D. (Physics and Mathematics), Assistant Professor, Head of the Department
28, Studencheskaya Str., 247760, Mozyr, Gomel region
A. D. Koral’kov
Mozyr State Pedagogical University named after I. P. Shamyakin
Belarus
Belarus
Koral’kov Artem D., Undergraduate
28, Studencheskaya Str., 247760, Mozyr, Gomel region
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