{
  "id": "math-ph/0312066",
  "version": "v1",
  "published": "2003-12-24T14:26:43.000Z",
  "updated": "2003-12-24T14:26:43.000Z",
  "title": "Spectral asymptotics of harmonic oscillator perturbed by bounded potential",
  "authors": [
    "M. Klein",
    "E. Korotyaev",
    "A. Pokrovski"
  ],
  "comment": "LaTeX, 39 pages, 2 postscript figures",
  "journal": "Annales Henri Poincare, V.6, No.4, pp.747-789,2005.",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "Consider the operator $ T=-{d^2dx^2}+x^2+q(x)$ in $L^2(\\mathbb{R})$, where real functions $q$, $q'$ and $\\int_0^xq(s)ds$ are bounded. In particular, $q$ is periodic or almost periodic. The spectrum of $T$ is purely discrete and consists of the simple eigenvalues $\\{\\mu_n\\}_{n=0}^\\infty$, $\\mu_n<\\mu_{n+1}$. We determine their asymptotics $\\mu_n = (2n+1) + (2\\pi)^{-1}\\int_{-\\pi}^{\\pi}q(\\sqrt{2n+1}\\sin\\theta)d\\theta + O(n^{-1/3})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-12-24T14:26:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34L20",
      "47N50"
    ],
    "keywords": [
      "harmonic oscillator",
      "spectral asymptotics",
      "bounded potential",
      "simple eigenvalues",
      "real functions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.ph..12066K"
    }
  }
}