{
  "id": "0909.3664",
  "version": "v2",
  "published": "2009-09-21T00:10:06.000Z",
  "updated": "2010-04-08T05:16:40.000Z",
  "title": "Equivalent Hermitian operator from supersymmetric quantum mechanics",
  "authors": [
    "Boris F. Samsonov",
    "V. V. Shamshutdinova",
    "A. V. Osipov"
  ],
  "comment": "9 pages; revised formula (14), published version with erratum",
  "journal": "Phys.Lett.A374:1962-1965,2010",
  "doi": "10.1016/j.physleta.2010.02.061",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "Diagonalizable pseudo-Hermitian Hamiltonians with real and discrete spectra, which are superpartners of Hermitian Hamiltonians, must be $\\eta$-pseudo-Hermitian with Hermitian, positive-definite and non-singular $\\eta$ operators. We show that despite the fact that an $\\eta$ operator produced by a supersymmetric transformation, corresponding to the exact supersymmetry, is singular, it can be used to find the eigenfunctions of a Hermitian operator equivalent to the given pseudo-Hermitian Hamiltonian. Once the eigenfunctions of the Hermitian operator are found the operator may be reconstructed with the help of the spectral decomposition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-04-08T05:16:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Ca",
      "03.65.Ge",
      "02.30.Tb"
    ],
    "keywords": [
      "supersymmetric quantum mechanics",
      "equivalent hermitian operator",
      "hermitian operator equivalent",
      "diagonalizable pseudo-hermitian hamiltonians",
      "discrete spectra"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Physics Letters A",
      "year": 2010,
      "month": "Apr",
      "volume": 374,
      "number": "19-20",
      "pages": 1962
    },
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 831782,
      "adsabs": "2010PhLA..374.1962S"
    }
  }
}