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      Lie theory and separation of variables. 7. The harmonic oscillator in elliptic coordinates and Ince polynomials

      Boyer, C.P.; Kalnins, Ernie G.; Miller, W., Jr.
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      Kalnins variables 7.pdf
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      DOI
       10.1063/1.522574
      Link
       link.aip.org
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      Boyer, C.P., Kalnins, E.G. & Miller, W., Jr. (1975). Lie theory and separation of variables. 7. The harmonic oscillator in elliptic coordinates and Ince polynomials. Journal of Mathematical Physics, 16, 512.
      Permanent Research Commons link: https://hdl.handle.net/10289/1243
      Abstract
      As a continuation of Paper 6 we study the separable basis eigenfunctions and their relationships for the harmonic oscillator Hamiltonian in two space variables with special emphasis on products of Ince polynomials, the eigenfunctions obtained when one separates variables in elliptic coordinates. The overlaps connecting this basis to the polar and Cartesian coordinate bases are obtained by computing in a simpler Bargmann Hilbert space model of the problem. We also show that Ince polynomials are intimately connected with the representation theory of SU (2), the group responsible for the eigenvalue degeneracy of the oscillator Hamiltonian.
      Date
      1975-03
      Type
      Journal Article
      Rights
      Copyright 1975 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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