{
  "id": "1012.0290",
  "version": "v4",
  "published": "2010-12-01T20:31:57.000Z",
  "updated": "2011-12-12T22:47:41.000Z",
  "title": "Supersymmetric Quantum Mechanics and Painlevé IV Equation",
  "authors": [
    "David Bermudez",
    "David J. Fernández C"
  ],
  "comment": "Proceedings of the Workshop 'Supersymmetric Quantum Mechanics and Spectral Design' (July 18-30, 2010, Benasque, Spain)",
  "journal": "SIGMA 7:025,2011",
  "doi": "10.3842/SIGMA.2011.025",
  "categories": [
    "math-ph",
    "hep-th",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "As it has been proven, the determination of general one-dimensional Schr\\\"odinger Hamiltonians having third-order differential ladder operators requires to solve the Painlev\\'e IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a simple technique for generating solutions of the Painlev\\'e IV equation. Finally, we classify these solutions into three relevant hierarchies.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-12-12T22:47:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supersymmetric quantum mechanics",
      "oscillator possess third-order differential ladder",
      "harmonic oscillator possess third-order differential",
      "possess third-order differential ladder operators"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "SIGMA",
      "year": 2011,
      "month": "Mar",
      "volume": 7,
      "pages": "025"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 878903,
      "adsabs": "2011SIGMA...7..025B"
    }
  }
}