{
  "id": "1205.0460",
  "version": "v1",
  "published": "2012-05-02T15:22:24.000Z",
  "updated": "2012-05-02T15:22:24.000Z",
  "title": "The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator",
  "authors": [
    "Tamas Palmai",
    "Barnabas Apagyi"
  ],
  "comment": "6 pages, 8 eps figures",
  "journal": "J. Phys. A: Math. Theor. 46 (2013) 045303",
  "doi": "10.1088/1751-8113/46/4/045303",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm-Liouville problem via the interpolation theory of the Weyl-Titchmarsh m-function. Then a Marchenko equation is solved to obtain the potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-02T15:22:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34L25",
      "65L09",
      "81U40"
    ],
    "keywords": [
      "auxiliary sturm-liouville operator",
      "marchenko equation",
      "fixed energy phase shifts",
      "quantum mechanical inverse scattering problem",
      "auxiliary sturm-liouville problem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2013,
      "month": "Feb",
      "volume": 46,
      "number": 4,
      "pages": "045303"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013JPhA...46d5303P"
    }
  }
}