{
  "id": "quant-ph/0410012",
  "version": "v3",
  "published": "2004-10-01T12:58:05.000Z",
  "updated": "2005-02-18T13:51:52.000Z",
  "title": "Pseudo-Hermitian Description of PT-Symmetric Systems Defined on a Complex Contour",
  "authors": [
    "Ali Mostafazadeh"
  ],
  "comment": "28 pages, 1 figure, revised version, to appear in J. Phys. A",
  "journal": "J.Phys. A38 (2005) 3213-3234",
  "categories": [
    "quant-ph",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We describe a method that allows for a practical application of the theory of pseudo-Hermitian operators to PT-symmetric systems defined on a complex contour. We apply this method to study the Hamiltonians $H=p^2+x^2(ix)^\\nu$ with $\\nu\\in(-2,\\infty)$ that are defined along the corresponding anti-Stokes lines. In particular, we reveal the intrinsic non-Hermiticity of $H$ for the cases that $\\nu$ is an even integer, so that $H=p^2\\pm x^{2+\\nu}$, and give a proof of the discreteness of the spectrum of $H$ for all $\\nu\\in(-2,\\infty)$. Furthermore, we study the consequences of defining a square-well Hamiltonian on a wedge-shaped complex contour. This yields a PT-symmetric system with a finite number of real eigenvalues. We present a comprehensive analysis of this system within the framework of pseudo-Hermitian quantum mechanics. We also outline a direct pseudo-Hermitian treatment of PT-symmetric systems defined on a complex contour which clarifies the underlying mathematical structure of the formulation of PT-symmetric quantum mechanics based on the charge-conjugation operator. Our results provide a conclusive evidence that pseudo-Hermitian quantum mechanics provides a complete description of general PT-symmetric systems regardless of whether they are defined along the real line or a complex contour.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2005-02-18T13:51:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.-w"
    ],
    "keywords": [
      "pt-symmetric systems",
      "complex contour",
      "pseudo-hermitian description",
      "pseudo-hermitian quantum mechanics",
      "direct pseudo-hermitian treatment"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0305-4470/38/14/011"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 661167,
      "adsabs": "2004quant.ph.10012M"
    }
  }
}