{
  "id": "math-ph/0401023",
  "version": "v1",
  "published": "2004-01-12T11:40:10.000Z",
  "updated": "2004-01-12T11:40:10.000Z",
  "title": "Necessary and sufficient conditions for existence of bound states in a central potential",
  "authors": [
    "Fabian Brau"
  ],
  "comment": "7 pages",
  "journal": "J. Phys. A36, 9907 (2003)",
  "doi": "10.1088/0305-4470/36/38/308",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP",
    "quant-ph"
  ],
  "abstract": "We obtain, using the Birman-Schwinger method, a series of necessary conditions for the existence of at least one bound state applicable to arbitrary central potentials in the context of nonrelativistic quantum mechanics. These conditions yield a monotonic series of lower limits on the \"critical\" value of the strength of the potential (for which a first bound state appears) which converges to the exact critical strength. We also obtain a sufficient condition for the existence of bound states in a central monotonic potential which yield an upper limit on the critical strength of the potential.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-01-12T11:40:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sufficient condition",
      "first bound state appears",
      "nonrelativistic quantum mechanics",
      "central monotonic potential",
      "arbitrary central potentials"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}