{
  "id": "1012.3357",
  "version": "v2",
  "published": "2010-12-15T15:09:29.000Z",
  "updated": "2011-01-14T13:59:44.000Z",
  "title": "Some Properties of an Infinite Family of Deformations of the Harmonic Oscillator",
  "authors": [
    "C. Quesne"
  ],
  "comment": "10 pages, no figure; to be published in Proceedings Symmetries in Nature: Symposium in Memoriam of Marcos Moshinsky, Cuernavaca, Mexico, Aug. 9-13, 2010",
  "journal": "Symmetries in Nature - Symposium in Memoriam of Marcos Moshinsky, AIP Conf. Proc., Vol. 1323, Amer. Inst. Phys., Melville, NY, 2010, 275-282",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "In memory of Marcos Moshinsky, who promoted the algebraic study of the harmonic oscillator, some results recently obtained on an infinite family of deformations of such a system are reviewed. This set, which was introduced by Tremblay, Turbiner, and Winternitz, consists in some Hamiltonians $H_k$ on the plane, depending on a positive real parameter $k$. Two algebraic extensions of $H_k$ are described. The first one, based on the elements of the dihedral group $D_{2k}$ and a Dunkl operator formalism, provides a convenient tool to prove the superintegrability of $H_k$ for odd integer $k$. The second one, employing two pairs of fermionic operators, leads to a supersymmetric extension of $H_k$ of the same kind as the familiar Freedman and Mende super-Calogero model. Some connection between both extensions is also outlined.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-14T13:59:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Ge",
      "11.30.Pb",
      "02.30.Rz",
      "02.30.Jr"
    ],
    "keywords": [
      "harmonic oscillator",
      "infinite family",
      "deformations",
      "properties",
      "mende super-calogero model"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "AIP Conf. Proc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010AIPC.1323..275Q"
    }
  }
}