{
  "id": "math-ph/0703049",
  "version": "v1",
  "published": "2007-03-14T23:09:13.000Z",
  "updated": "2007-03-14T23:09:13.000Z",
  "title": "High energy eigenfunctions of one-dimensional Schrodinger operators with polynomial potentials",
  "authors": [
    "Alexandre Eremenko",
    "Andrei Gabrielov",
    "Boris Shapiro"
  ],
  "comment": "22 pages, 9 figures",
  "journal": "Computational Methods and Function Theory, 8 (2008). No. 2, 513--529.",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "For a class of one-dimensional Schrodinger operators with polynomial potentials that includes Hermitian and PT-symmetric operators, we show that the zeros of scaled eigenfunctions have a limit disctibution in the complex plane as the eigenvalues tend to infinity. This limit distribution depends only on the degree of potential and on the boundary conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-14T23:09:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34B05",
      "34L20",
      "34M40",
      "34M60"
    ],
    "keywords": [
      "one-dimensional schrodinger operators",
      "high energy eigenfunctions",
      "polynomial potentials",
      "limit distribution depends",
      "pt-symmetric operators"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math.ph...3049E"
    }
  }
}