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      Models for the 3D Singular Isotropic Oscillator Quadratic Algebra

      Kalnins, Ernie G.; Miller, W., Jr.; Post, Sarah
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      3DoscillatorGroup27.pdf
      Accepted version, 157.1Kb
      DOI
       10.1134/S1063778810020249
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      Kalnins, E. G., Miller, W., Jr., & Post, S. (2010). Models for the 3D Singular Isotropic Oscillator Quadratic Algebra. Physics of Atomic Nuclei, 73(2), 359–366. http://doi.org/10.1134/S1063778810020249
      Permanent Research Commons link: https://hdl.handle.net/10289/10148
      Abstract
      We give the first explicit construction of the quadratic algebra for a 3D quantum superintegrable system with nondegenerate (4-parameter) potential together with realizations of irreducible representations of the quadratic algebra in terms of differential—differential or differential—difference and difference—difference operators in two variables. The example is the singular isotropic oscillator. We point out that the quantum models arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras for superintegrable systems in n dimensions and are closely related to Hecke algebras and multivariable orthogonal polynomials.
      Date
      2010-02-01
      Type
      Journal Article
      Publisher
      MAIK NAUKA/INTERPERIODICA/SPRINGER
      Rights
      This is an author’s accepted version of an article published in the journal: Physics of Atomic Nuclei. © Pleiades Publishing, Ltd., 2010.
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      • Computing and Mathematical Sciences Papers [1455]
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