{
  "id": "math-ph/0310035",
  "version": "v1",
  "published": "2003-10-17T16:09:13.000Z",
  "updated": "2003-10-17T16:09:13.000Z",
  "title": "Bound states in two spatial dimensions in the non-central case",
  "authors": [
    "Andre Martin",
    "Tai Tsun Wu"
  ],
  "comment": "Work supported in part by the U.S. Department of Energy under Grant No. DE-FG02-84-ER40158",
  "journal": "J.Math.Phys. 45 (2004) 922-931",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting the number of bound states in a potential gV for g=1 is replaced by counting the number of g_i's for which zero energy bound states exist, and then the kernel of the integral equation for the zero-energy wave functon is symmetrized. One of the keys of the solution is the replacement of an inhomogeneous integral equation by a homogeneous integral equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-17T16:09:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Ge",
      "02.30.Rz"
    ],
    "keywords": [
      "spatial dimensions",
      "non-central case",
      "zero energy bound states",
      "zero-energy wave functon",
      "negative energy bound states"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Journal of Mathematical Physics",
      "doi": "10.1063/1.1639956",
      "year": 2004,
      "month": "Mar",
      "volume": 45,
      "number": 3,
      "pages": 922
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 631122,
      "adsabs": "2004JMP....45..922M"
    }
  }
}