Adding Potentials to Superintegrable Systems with Symmetry
Exactly Solvable and Integrable Systems
2021-06-09 v1 Mathematical Physics
math.MP
Abstract
In previous work, we have considered Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. Previously our Hamiltonians have represented free motion, but here we consider the problem of adding potential functions in the presence of symmetry. Separable potentials in the 3 dimensional space reduce to 3 or 4 parameter potentials for Darboux-Koenigs Hamiltonians. Other 3D coordinate systems reveal connections between Darboux-Koenigs and other well known super-integrable Hamiltonians, such as the Kepler problem and isotropic oscillator.
Cite
@article{arxiv.2009.11653,
title = {Adding Potentials to Superintegrable Systems with Symmetry},
author = {Allan P. Fordy and Qing Huang},
journal= {arXiv preprint arXiv:2009.11653},
year = {2021}
}
Comments
22 pages, 3 tables. arXiv admin note: text overlap with arXiv:1910.08836