{
  "id": "math-ph/0402023",
  "version": "v1",
  "published": "2004-02-10T08:06:17.000Z",
  "updated": "2004-02-10T08:06:17.000Z",
  "title": "On the decrease of the number of bound states with the increase of the angular momentum",
  "authors": [
    "Fabian Brau"
  ],
  "journal": "Phys. Lett. A322, 67 (2004)",
  "doi": "10.1016/j.physleta.2004.01.005",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "For the class of central potentials possessing a finite number of bound states and for which the second derivative of $r V(r)$ is negative, we prove, using the supersymmetric quantum mechanics formalism, that an increase of the angular momentum $\\ell$ by one unit yields a decrease of the number of bound states of at least one unit: $N_{\\ell+1}\\le N_{\\ell}-1$. This property is used to obtain, for this class of potential, an upper limit on the total number of bound states which significantly improves previously known results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-10T08:06:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bound states",
      "angular momentum",
      "supersymmetric quantum mechanics formalism",
      "central potentials",
      "finite number"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}