1. [formula omitted]-Smorodinsky–Winternitz system in a constant magnetic field.
- Author
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Shmavonyan, Hovhannes
- Subjects
- *
MAGNETIC fields - Abstract
Abstract We propose the superintegrable generalization of Smorodinsky–Winternitz system on the N -dimensional complex Euclidian space which is specified by the presence of constant magnetic field. We find out that in addition to 2 N Liouville integrals the system has additional functionally independent constants of motion, and compute their symmetry algebra. We perform the Kustaanheimo–Stiefel transformation of C 2 -Smorodinsky–Winternitz system to the (three-dimensional) generalized MICZ-Kepler problem and find the symmetry algebra of the latter one. We observe that constant magnetic field appearing in the initial system has no qualitative impact on the resulting system. Highlights • We review the properties of (RN-)Smorodinsky–Winternitz system, presenting expressions of its symmetry generators, symmetry algebra, wavefunctions and Energy spectrum. • We present CN-Smorodinsky–Winternitz system in a constant magnetic field, find the expressions of its constants of motion, compute their algebra and quantize the system. • We perform Kustaanheimo–Stieffel transformation of the C2-Smorodinsky–Winternitz system and obtain, in this way, the so-called "generalized MICZ-Kepler system". • We discuss the obtained results and possibilities of generalizations, namely supersymmetrization and quaternionic and curved background generalizations. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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