{
  "id": "1304.3295",
  "version": "v2",
  "published": "2013-04-11T13:37:56.000Z",
  "updated": "2013-07-17T07:02:50.000Z",
  "title": "The oscillator model for the Lie superalgebra sh(2|2) and Charlier polynomials",
  "authors": [
    "E. I. Jafarov",
    "J. Van der Jeugt"
  ],
  "comment": "Minor changes and some additional references added in version 1",
  "journal": "J. Math. Phys. 54 (2013) 103506",
  "doi": "10.1063/1.4824742",
  "categories": [
    "math-ph",
    "math.MP",
    "math.RT",
    "quant-ph"
  ],
  "abstract": "We investigate an algebraic model for the quantum oscillator based upon the Lie superalgebra sh(2|2), known as the Heisenberg-Weyl superalgebra or \"the algebra of supersymmetric quantum mechanics\", and its Fock representation. The model offers some freedom in the choice of a position and a momentum operator, leading to a free model parameter gamma. Using the technique of Jacobi matrices, we determine the spectrum of the position operator, and show that its wavefunctions are related to Charlier polynomials C_n with parameter gamma^2. Some properties of these wavefunctions are discussed, as well as some other properties of the current oscillator model.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-17T07:02:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81R05",
      "81Q10",
      "81Q80",
      "33C45",
      "03.65.Fd",
      "03.65.Ta",
      "02.10.De",
      "02.10.Ud"
    ],
    "keywords": [
      "lie superalgebra",
      "charlier polynomials",
      "free model parameter gamma",
      "current oscillator model",
      "supersymmetric quantum mechanics"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "year": 2013,
      "month": "Oct",
      "volume": 54,
      "number": 10,
      "pages": 3506
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JMP....54j3506J"
    }
  }
}