{
  "id": "1412.5874",
  "version": "v2",
  "published": "2014-12-18T14:30:38.000Z",
  "updated": "2015-04-15T13:01:24.000Z",
  "title": "Ladder operators for solvable potentials connected with exceptional orthogonal polynomials",
  "authors": [
    "C. Quesne"
  ],
  "comment": "14 pages, no figure, communication at the XXXth International Colloquium on Group Theoretical Methods in Physics, 14-18 July, 2014, Ghent, Belgium, published version",
  "journal": "J. Phys. Conf. Ser. 597 (2015) 012064",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI",
    "quant-ph"
  ],
  "abstract": "Exceptional orthogonal polynomials constitute the main part of the bound-state wavefunctions of some solvable quantum potentials, which are rational extensions of well-known shape-invariant ones. The former potentials are most easily built from the latter by using higher-order supersymmetric quantum mechanics (SUSYQM) or Darboux method. They may in general belong to three different types (or a mixture of them): types I and II, which are strictly isospectral, and type III, for which k extra bound states are created below the starting potential spectrum. A well-known SUSYQM method enables one to construct ladder operators for the extended potentials by combining the supercharges with the ladder operators of the starting potential. The resulting ladder operators close a polynomial Heisenberg algebra (PHA) with the corresponding Hamiltonian. In the special case of type III extended potentials, for this PHA the k extra bound states form k singlets isolated from the higher excited states. Some alternative constructions of ladder operators are reviewed. Among them, there is one that combines the state-adding and state-deleting approaches to type III extended potentials (or so-called Darboux-Crum and Krein-Adler transformations) and mixes the k extra bound states with the higher excited states. This novel approach can be used for building integrals of motion for two-dimensional superintegrable systems constructed from rationally-extended potentials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-18T14:30:38.000Z",
      "comment": "14 pages, no figure, communication at the XXXth International Colloquium on Group Theoretical Methods in Physics, 14-18 July, 2014, Ghent, Belgium, to appear in Proceedings",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-15T13:01:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ladder operators",
      "solvable potentials",
      "extended potentials",
      "higher excited states",
      "extra bound states form"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1742-6596/597/1/012064",
      "journal": "Journal of Physics Conference Series",
      "year": 2015,
      "month": "Apr",
      "volume": 597,
      "number": 1,
      "pages": "012064"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JPhCS.597a2064Q"
    }
  }
}