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      Superintegrability on the two-dimensional hyperboloid

      Kalnins, Ernie G.; Miller, W., Jr.; Pogosyan, G.S.
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      Kalnins Superintegrability on the two-dimensional hyperboloid.pdf
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      DOI
       10.1063/1.531951
      Link
       link.aip.org
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      Citation
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      Kalnins, E.G., Miller, W., Jr. & Pogosyan, G.S. (1997). Superintegrability on the two-dimensional hyperboloid. Journal of Mathematical Physics, 38, 5416.
      Permanent Research Commons link: https://hdl.handle.net/10289/1199
      Abstract
      In this work we examine the basis functions for classical and quantum mechanical systems on the two-dimensional hyperboloid that admit separation of variables in at least two coordinate systems. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup spherical coordinate cases, and the details of the structure of the quadratic symmetry algebras.
      Date
      1997-10
      Type
      Journal Article
      Publisher
      American Institute of Physics
      Rights
      Copyright 1997 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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      • Computing and Mathematical Sciences Papers [1455]
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