{
  "id": "1410.4030",
  "version": "v1",
  "published": "2014-10-15T12:07:23.000Z",
  "updated": "2014-10-15T12:07:23.000Z",
  "title": "On the Classical Limit of the Schrödinger Equation",
  "authors": [
    "Claude Bardos",
    "François Golse",
    "Peter Markowich",
    "Thierry Paul"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "This paper provides an elementary proof of the classical limit of the Schr\\\"{o}dinger equation with WKB type initial data and over arbitrary long finite time intervals. We use only the stationary phase method and the Laptev-Sigal simple and elegant construction of a parametrix for Schr\\\"{o}dinger type equations [A. Laptev, I. Sigal, Review of Math. Phys. 12 (2000), 749-766]. We also explain in detail how the phase shifts across caustics obtained when using the Laptev-Sigal parametrix are related to the Maslov index.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-15T12:07:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q41",
      "81Q20",
      "35S30",
      "53D12"
    ],
    "keywords": [
      "classical limit",
      "schrödinger equation",
      "arbitrary long finite time intervals",
      "wkb type initial data",
      "stationary phase method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.4030B"
    }
  }
}