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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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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Abstract 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.
AbstractList 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.
Author Huang, Qing
Fordy, Allan P.
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10.1088/1751-8113/46/42/423001
10.1088/1751-8121/ab9edd
10.1103/PhysRevA.41.5666
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10.1016/j.aop.2009.03.001
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10.1103/RevModPhys.86.1283
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10.1007/978-1-4684-9946-9
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