On the symmetry algebra of a one-dimensional quantum-mechanical oscillator on a hyperbola
https://doi.org/10.29235/1561-2430-2024-60-1-34-42
Abstract
The quantum-mechanical problem of a harmonic oscillator on a hyperbola as a one-dimensional space of constant negative curvature is considered in this article. A generalization to the singular oscillator model in the context of one-dimensional Cayley – Klein geometries is given by the factorization method. The energy spectrum and wave functions of stationary states are found having the curvature of space as a parameter. For the energy levels of the singular oscillator, the effect of non-zero curvature is clearly manifested through a positive or negative term, depending on the sign of the curvature, which is quadratic in the level number. The results obtained are consistent with those previously published. The dynamical symmetry of the problem is shown explicitly as a quadratic Hahn algebra QH(3) or its isomorphic Higgs algebra.
About the Authors
A. N. Lavrenov
Belarusian State Pedagogical University named after Maxim Tank
Belarus
Belarus
Alexandre N. Lavrenov – Ph. D. (Physics and Mathe matics), Associate Professor, Associate Professor of the Department of Informatics and Methods of Teaching Infor matics
18, Sovetskaya Str., 220050, Minsk
I. A. Lavrenov
Octonion technology Ltd
Belarus
Belarus
Ivan А. Lavrenov – Leading Specialist
25, Y. Kupala Str., 220030, Minsk
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