{
  "id": "1612.07692",
  "version": "v1",
  "published": "2016-12-22T16:49:23.000Z",
  "updated": "2016-12-22T16:49:23.000Z",
  "title": "A finite oscillator model with equidistant position spectrum based on an extension of $\\mathfrak{su}(2)$",
  "authors": [
    "Roy Oste",
    "Joris Van der Jeugt"
  ],
  "comment": "This is a preprint of a paper whose final and definite form is in Journal of Physics A: Mathematical and Theoretical",
  "journal": "J. Phys. A: Math. Theor. 49 175204 (2016)",
  "doi": "10.1088/1751-8113/49/17/175204",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We consider an extension of the real Lie algebra $\\mathfrak{su}(2)$ by introducing a parity operator $P$ and a parameter $c$. This extended algebra is isomorphic to the Bannai-Ito algebra with two parameters equal to zero. For this algebra we classify all unitary finite-dimensional representations and show their relation with known representations of $\\mathfrak{su}(2)$. Moreover, we present a model for a one-dimensional finite oscillator based on the odd-dimensional representations of this algebra. For this model, the spectrum of the position operator is equidistant and coincides with the spectrum of the known $\\mathfrak{su}(2)$ oscillator. In particular the spectrum is independent of the parameter $c$ while the discrete position wavefunctions, which are given in terms of certain dual Hahn polynomials, do depend on this parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-22T16:49:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equidistant position spectrum",
      "finite oscillator model",
      "real lie algebra",
      "unitary finite-dimensional representations",
      "one-dimensional finite oscillator"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "IOP"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}