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.

9 pages, no figures

References in corpus (5)

• Reduction of superintegrable systems: the anisotropic harmonic oscillator
• Superintegrability of the Caged Anisotropic Oscillator
• Superintegrability on N-dimensional curved spaces: Central potentials, centrifugal terms and monopoles
• A maximally superintegrable system on an n-dimensional space of nonconstant curvature
• A New Superintegrable Hamiltonian

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