https://doi.org/10.1140/epjp/s13360-023-04524-x
Regular Article
Quantum, classical symmetries, and action-angle variables by factorization of superintegrable systems
1
Department of Physics, Faculty of Science, Ankara University, 06100, Ankara, Turkey
2
Departamento de Física Teórica, Atómica y Óptica, and IMUVA, Universidad de Valladolid, 47011, Valladolid, Spain
Received:
19
May
2023
Accepted:
26
September
2023
Published online:
19
October
2023
The purpose of this work is to present a method based on the factorizations used in one-dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this procedure to the harmonic oscillator and Kepler–Coulomb systems to show the differences with other more standard approaches. We describe in detail the basic ingredients to make explicit the parallelism of classical and quantum treatments. One of the most interesting results is the finding of action-angle variables as a natural component of the classical symmetries within this formalism.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
