{
  "id": "0805.0503",
  "version": "v2",
  "published": "2008-05-05T10:20:36.000Z",
  "updated": "2008-05-30T16:48:09.000Z",
  "title": "Levy processes and Schroedinger equation",
  "authors": [
    "Nicola Cufaro Petroni",
    "Modesto Pusterla"
  ],
  "comment": "10 pages; changed the TeX documentclass; added references [21] and [22] and comments about them; changed definitions (11) and (12); added acknowledgments; small changes scattered in the text",
  "journal": "Phys A 388 (2009) 824",
  "doi": "10.1016/j.physa.2008.11.035",
  "categories": [
    "cond-mat.stat-mech",
    "math.PR",
    "quant-ph"
  ],
  "abstract": "We analyze the extension of the well known relation between Brownian motion and Schroedinger equation to the family of Levy processes. We consider a Levy-Schroedinger equation where the usual kinetic energy operator - the Laplacian - is generalized by means of a selfadjoint, pseudodifferential operator whose symbol is the logarithmic characteristic of an infinitely divisible law. The Levy-Khintchin formula shows then how to write down this operator in an integro--differential form. When the underlying Levy process is stable we recover as a particular case the fractional Schroedinger equation. A few examples are finally given and we find that there are physically relevant models (such as a form of the relativistic Schroedinger equation) that are in the domain of the non-stable, Levy-Schroedinger equations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-05-30T16:48:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "levy processes",
      "levy-schroedinger equation",
      "usual kinetic energy operator",
      "relativistic schroedinger equation",
      "fractional schroedinger equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Physica A Statistical Mechanics and its Applications",
      "year": 2009,
      "month": "Mar",
      "volume": 388,
      "number": 6,
      "pages": 824
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009PhyA..388..824C"
    }
  }
}