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

Miguel A. Rodriguez, Piergiulio Tempesta

Published 2022-10-05Version 1

We introduce a large 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, such that this new Hamiltonian family is superintegrable.