{
  "id": "1303.7150",
  "version": "v3",
  "published": "2013-03-28T15:33:53.000Z",
  "updated": "2013-10-11T12:49:51.000Z",
  "title": "New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems",
  "authors": [
    "I. Marquette",
    "C. Quesne"
  ],
  "comment": "22 pages, published version",
  "journal": "J. Math. Phys. 54 (2013) 102102, 12 pages",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI",
    "quant-ph"
  ],
  "abstract": "New ladder operators are constructed for a rational extension of the harmonic oscillator associated with type III Hermite exceptional orthogonal polynomials and characterized by an even integer $m$. The eigenstates of the Hamiltonian separate into $m+1$ infinite-dimensional unitary irreducible representations of the corresponding polynomial Heisenberg algebra. These ladder operators are used to construct a higher-order integral of motion for two superintegrable two-dimensional systems separable in cartesian coordinates. The polynomial algebras of such systems provide for the first time an algebraic derivation of the whole spectrum through their finite-dimensional unitary irreducible representations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-11T12:49:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Ge",
      "02.10.De",
      "02.10.Ud",
      "03.65.Fd"
    ],
    "keywords": [
      "ladder operators",
      "rational extension",
      "harmonic oscillator",
      "two-dimensional systems",
      "hermite exceptional orthogonal polynomials"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "doi": "10.1063/1.4823771",
      "year": 2013,
      "month": "Oct",
      "volume": 54,
      "number": 10,
      "pages": 2102
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JMP....54j2102M"
    }
  }
}