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Mathematical Physics

arXiv:2210.02208 (math-ph)
[Submitted on 5 Oct 2022 (v1), last revised 20 Dec 2022 (this version, v2)]

Title:On higher-dimensional superintegrable systems: A new family of classical and quantum Hamiltonian models

Authors:Miguel A. Rodriguez, Piergiulio Tempesta
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Abstract:We introduce a family of $n$-dimensional Hamiltonian systems which, contain, as special reductions, several superintegrable systems as the Tremblay-Turbiner-Winternitz system, a generalized Kepler potential and the anisotropic harmonic oscillator with Rosochatius terms. We conjecture that there exist special values in the space of parameters, apart from those leading to known cases, for which this new Hamiltonian family is superintegrable.
Comments: 9 pages, no figures
Subjects: Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)
MSC classes: 70H06
Cite as: arXiv:2210.02208 [math-ph]
  (or arXiv:2210.02208v2 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.2210.02208
Related DOI: https://doi.org/10.1088/1751-8121/acaada

Submission history

From: Piergiulio Tempesta [view email]
[v1] Wed, 5 Oct 2022 12:35:20 UTC (10 KB)
[v2] Tue, 20 Dec 2022 10:04:26 UTC (10 KB)
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