{
  "id": "0906.0142",
  "version": "v2",
  "published": "2009-05-31T08:49:32.000Z",
  "updated": "2009-08-22T05:01:43.000Z",
  "title": "Infinitely many shape invariant potentials and new orthogonal polynomials",
  "authors": [
    "Satoru Odake",
    "Ryu Sasaki"
  ],
  "comment": "4 pages; published in Phys.Lett.B, two references and comments added, eqs.(34)(35)(45)(46) simplified",
  "journal": "Phys.Lett.B679:414-417,2009",
  "doi": "10.1016/j.physletb.2009.08.004",
  "categories": [
    "math-ph",
    "hep-th",
    "math.CA",
    "math.MP",
    "nlin.SI",
    "quant-ph"
  ],
  "abstract": "Three sets of exactly solvable one-dimensional quantum mechanical potentials are presented. These are shape invariant potentials obtained by deforming the radial oscillator and the trigonometric/hyperbolic P\\\"oschl-Teller potentials in terms of their degree \\ell polynomial eigenfunctions. We present the entire eigenfunctions for these Hamiltonians (\\ell=1,2,...) in terms of new orthogonal polynomials. Two recently reported shape invariant potentials of Quesne and G\\'omez-Ullate et al's are the first members of these infinitely many potentials.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-08-22T05:01:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.-w",
      "02.30.Gp",
      "03.65.Ge",
      "02.30.Ik",
      "03.65.Fd",
      "03.65.Ca"
    ],
    "keywords": [
      "orthogonal polynomials",
      "reported shape invariant potentials",
      "solvable one-dimensional quantum mechanical potentials",
      "exactly solvable one-dimensional quantum"
    ],
    "tags": [
      "journal article",
      "famous paper"
    ],
    "publication": {
      "journal": "Physics Letters B",
      "year": 2009,
      "month": "Aug",
      "volume": 679,
      "number": 4,
      "pages": 414
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 821880,
      "adsabs": "2009PhLB..679..414O"
    }
  }
}