{
  "id": "0711.0879",
  "version": "v1",
  "published": "2007-11-06T14:01:50.000Z",
  "updated": "2007-11-06T14:01:50.000Z",
  "title": "Resolvent and scattering matrix at the maximum of the potential",
  "authors": [
    "Ivana Alexandrova",
    "Jean-Francois Bony",
    "Thierry Ramond"
  ],
  "comment": "31 pages, 3 figures",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the microlocal structure of the resolvent of the semi-classical Schrodinger operator with short range potential at an energy which is a unique non-degenerate global maximum of the potential. We prove that it is a semi-classical Fourier integral operator quantizing the incoming and outgoing Lagrangian submanifolds associated to the fixed hyperbolic point. We then discuss two applications of this result to describing the structure of the spectral function and the scattering matrix of the Schrodinger operator at the critical energy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-06T14:01:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35P25",
      "81U20",
      "35S30",
      "47A10",
      "35B38"
    ],
    "keywords": [
      "scattering matrix",
      "unique non-degenerate global maximum",
      "short range potential",
      "semi-classical schrodinger operator",
      "semi-classical fourier integral operator quantizing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.0879A"
    }
  }
}