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arXiv · 2009.11653

Adding Potentials to Superintegrable Systems with Symmetry

Allan P. Fordy·Qing Huang
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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.

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BibTeXRIS

Allan P. Fordy, Qing Huang. 2020-09-22. Adding Potentials to Superintegrable Systems with Symmetry. https://doi.org/10.1098/rspa.2020.0800

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