{
  "id": "math-ph/0207025",
  "version": "v2",
  "published": "2002-07-19T08:27:30.000Z",
  "updated": "2002-11-14T15:50:54.000Z",
  "title": "Bound states due to a strong $δ$ interaction supported by a curved surface",
  "authors": [
    "Pavel Exner",
    "Sylwia Kondej"
  ],
  "comment": "LaTeX 2e, 21 pages",
  "journal": "J. Phys. A36 (2003), 443-457",
  "doi": "10.1088/0305-4470/36/2/311",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the Schr\\\"odinger operator $-\\Delta -\\alpha \\delta (x-\\Gamma)$ in $L^2(\\R^3)$ with a $\\delta$ interaction supported by an infinite non-planar surface $\\Gamma$ which is smooth, admits a global normal parameterization with a uniformly elliptic metric. We show that if $\\Gamma $ is asymptotically planar in a suitable sense and $\\alpha>0$ is sufficiently large this operator has a non-empty discrete spectrum and derive an asymptotic expansion of the eigenvalues in terms of a ``two-dimensional'' comparison operator determined by the geometry of the surface $\\Gamma$. [A revised version, to appear in J. Phys. A]",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-11-14T15:50:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "interaction",
      "bound states",
      "curved surface",
      "infinite non-planar surface",
      "non-empty discrete spectrum"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2003,
      "month": "Jan",
      "volume": 36,
      "number": 2,
      "pages": 443
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003JPhA...36..443E"
    }
  }
}