{
  "id": "1211.0308",
  "version": "v1",
  "published": "2012-11-01T21:05:50.000Z",
  "updated": "2012-11-01T21:05:50.000Z",
  "title": "$θ(\\hat{x},\\hat{p})-$deformation of the harmonic oscillator in a $2D-$phase space",
  "authors": [
    "M. N. Hounkonnou",
    "D. Ousmane Samary",
    "E. Baloitcha",
    "S. Arjika"
  ],
  "comment": "9 pages",
  "journal": "Geometric Methods in Physics Trends in Mathematics 2013, pp 29-37",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "This work addresses a ${\\theta}(\\hat{x},\\hat{p})-$deformation of the harmonic oscillator in a $2D-$phase space. Specifically, it concerns a quantum mechanics of the harmonic oscillator based on a noncanonical commutation relation depending on the phase space coordinates. A reformulation of this deformation is considered in terms of a $q-$deformation allowing to easily deduce the energy spectrum of the induced deformed harmonic oscillator. Then, it is proved that the deformed position and momentum operators admit a one-parameter family of self-adjoint extensions. These operators engender new families of deformed Hermite polynomials generalizing usual $q-$ Hermite polynomials. Relevant matrix elements are computed. Finally, a $su(2)-$algebra representation of the considered deformation is investigated and discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-01T21:05:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic oscillator",
      "deformation",
      "momentum operators admit",
      "phase space coordinates",
      "relevant matrix elements"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/978-3-0348-0645-9_3"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1336697,
      "adsabs": "2012arXiv1211.0308H"
    }
  }
}