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      Superintegrable systems in Darboux spaces

      Kalnins, Ernie G.; Kress, Jonathan M.; Miller, W., Jr.
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      Kalnins superintegrable.pdf
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      DOI
       10.1063/1.1619580
      Link
       link.aip.org
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      Citation
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      Kalnins, E.G., Kress, J.M. & Miller, W., Jr. (2003). Superintegrable systems in Darboux spaces. Journal of Mathematical Physics, 44, 5811.
      Permanent Research Commons link: https://hdl.handle.net/10289/1185
      Abstract
      Almost all research on superintegrable potentials concerns spaces of constant curvature. In this paper we find by exhaustive calculation, all superintegrable potentials in the four Darboux spaces of revolution that have at least two integrals of motion quadratic in the momenta, in addition to the Hamiltonian. These are two-dimensional spaces of nonconstant curvature. It turns out that all of these potentials are equivalent to superintegrable potentials in complex Euclidean 2-space or on the complex 2-sphere, via "coupling constant metamorphosis" (or equivalently, via Stäckel multiplier transformations). We present a table of the results.
      Date
      2003-12
      Type
      Journal Article
      Publisher
      American Institute of Physics
      Rights
      Copyright 2003 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jsp
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