{
  "id": "1010.5521",
  "version": "v2",
  "published": "2010-10-26T21:00:15.000Z",
  "updated": "2010-11-02T19:39:39.000Z",
  "title": "The quantum Arnold transformation",
  "authors": [
    "Victor Aldaya",
    "Francisco Cossio",
    "Julio Guerrero",
    "Francisco F. Lopez-Ruiz"
  ],
  "comment": "19 pages, minor changes, references updated",
  "journal": "J. Phys. A: Math. Theor. 44, 065302 (2011)",
  "doi": "10.1088/1751-8113/44/6/065302",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with friction linear in velocity, can be related to the quantum free-particle dynamical system. This transformation provides a basic (Heisenberg-Weyl) algebra of quantum operators, along with well-defined Hermitian operators which can be chosen as evolution-like observables and complete the entire Schr\\\"odinger algebra. It also proves to be very helpful in performing certain computations quickly, to obtain, for example, wave functions and closed analytic expressions for time-evolution operators.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-11-02T19:39:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum arnold transformation",
      "linear second-order ordinary differential equations",
      "non-homogeneous linear second-order ordinary differential",
      "quantum free-particle dynamical system"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2011,
      "month": "Feb",
      "volume": 44,
      "number": 6,
      "pages": "065302"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JPhA...44f5302A"
    }
  }
}