{
  "id": "0808.3149",
  "version": "v9",
  "published": "2008-08-22T21:37:15.000Z",
  "updated": "2009-03-08T17:05:19.000Z",
  "title": "The Time Inversion for Modified Oscillators",
  "authors": [
    "Ricardo Cordero-Soto",
    "Sergei K. Suslov"
  ],
  "comment": "33 pages, four figures, and two tables",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We discuss a new completely integrable case of the time-dependent Schroedinger equation in $R^n$ with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator recently considered by Meiler, Cordero-Soto, and Suslov. A second pair of dual Hamiltonians is also found in the momentum representation. Our examples show that in mathematical physics and quantum mechanics a change in the direction of time may require a total change of the system dynamics in order to return the system back to its original quantum state. Particular solutions of the corresponding Schroedinger equations are also obtained. A Hamiltonian structure of the classical integrable problem and its quantization are also discussed.",
  "revisions": [
    {
      "version": "v9",
      "updated": "2009-03-08T17:05:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time inversion",
      "modified oscillator",
      "time-dependent schroedinger equation",
      "original quantum state",
      "quantum oscillator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.3149C"
    }
  }
}