{
  "id": "math/0306218",
  "version": "v1",
  "published": "2003-06-13T12:24:37.000Z",
  "updated": "2003-06-13T12:24:37.000Z",
  "title": "Convergence of an exact quantization scheme",
  "authors": [
    "Artur Avila"
  ],
  "comment": "10 pages, no figures, first version",
  "doi": "10.1007/s00220-004-1112-9",
  "categories": [
    "math.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "It has been shown by Voros \\cite {V} that the spectrum of the one-dimensional homogeneous anharmonic oscillator (Schr\\\"odinger operator with potential $q^{2M}$, $M>1$) is a fixed point of an explicit non-linear transformation. We show that this fixed point is globally and exponentially attractive in spaces of properly normalized sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-06-13T12:24:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exact quantization scheme",
      "convergence",
      "explicit non-linear transformation",
      "one-dimensional homogeneous anharmonic oscillator",
      "fixed point"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2004,
      "volume": 249,
      "number": 2,
      "pages": 305
    },
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004CMaPh.249..305A"
    }
  }
}