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

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.

arXiv comment9 pages, no figures

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Cited by in corpus (2)

• Superintegrability and Deformed Oscillator Realizations of Quantum TTW Hamiltonians on Constant-Curvature Manifolds and with Reflections in a Plane
• Superintegrable families of magnetic monopoles with non-radial potential in curved background