Adding potentials to superintegrable systems with symmetry

In previous work, we have considered Hamiltonians associated with three-dimensional conformally flat spaces, possessing two-, three- and four-dimensional isometry algebras. Previously, our Hamiltonians have represented free motion, but here we consider the problem of adding potential functions in th...

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Bibliographic Details
Published inProceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 477; no. 2248
Main Authors Fordy, Allan P., Huang, Qing
Format Journal Article
LanguageEnglish
Published 01.04.2021
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Summary:In previous work, we have considered Hamiltonians associated with three-dimensional conformally flat spaces, possessing two-, three- and four-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 three-dimensional space reduce to 3 or 4 parameter potentials for Darboux–Koenigs Hamiltonians. Other three-dimensional coordinate systems reveal connections between Darboux–Koenigs and other well-known super-integrable Hamiltonians, such as the Kepler problem and isotropic oscillator.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2020.0800