{
  "id": "1305.6307",
  "version": "v1",
  "published": "2013-05-27T19:57:03.000Z",
  "updated": "2013-05-27T19:57:03.000Z",
  "title": "Generalized space and linear momentum operators in quantum mechanics",
  "authors": [
    "Bruno G. da Costa",
    "Ernesto P. Borges"
  ],
  "comment": "5 pages, 4 figures (12 eps files)",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We propose a modification of a recently introduced generalized translation operator, by including a $q$-exponential factor, which implies in the definition of a Hermitian deformed linear momentum operator $\\hat{p}_q$, and its canonically conjugate deformed position operator $\\hat{x}_q$. A canonical transformation leads the Hamiltonian of a position-dependent mass particle to another Hamiltonian of a particle with constant mass in a conservative force field of a deformed phase space. The equation of motion for the classical phase space may be expressed in terms of the generalized dual $q$-derivative. A position-dependent mass confined in an infinite square potential well is shown as an instance. Uncertainty and correspondence principles are analyzed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-27T19:57:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum mechanics",
      "generalized space",
      "phase space",
      "hermitian deformed linear momentum operator",
      "position-dependent mass particle"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1063/1.4884299",
      "journal": "Journal of Mathematical Physics",
      "year": 2014,
      "month": "Jun",
      "volume": 55,
      "number": 6,
      "pages": "062105"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014JMP....55f2105D"
    }
  }
}