{
  "id": "0902.3744",
  "version": "v1",
  "published": "2009-02-21T19:33:18.000Z",
  "updated": "2009-02-21T19:33:18.000Z",
  "title": "Pseudo-Boson Coherent and Fock States",
  "authors": [
    "D. A. Trifonov"
  ],
  "comment": "10 pages, no figures. Based on talk given at 9th IC on Complex Structures, Integrability and Vector Fields, Sofia, August 2008",
  "journal": "in Differential Geometry, Complex Analysis and Mathematical Physics, eds. K. Sekigawa et al (W. Scientific 2009), pp. 241-250",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Coherent states (CS) for non-Hermitian systems are introduced as eigenstates of pseudo-Hermitian boson annihilation operators. The set of these CS includes two subsets which form bi-normalized and bi-overcomplete system of states. The subsets consist of eigenstates of two complementary lowering pseudo-Hermitian boson operators. Explicit constructions are provided on the example of one-parameter family of pseudo-boson ladder operators. The wave functions of the eigenstates of the two complementary number operators, which form a bi-orthonormal system of Fock states, are found to be proportional to new polynomials, that are bi-orthogonal and can be regarded as a generalization of standard Hermite polynomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-21T19:33:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fock states",
      "pseudo-boson coherent",
      "complementary lowering pseudo-hermitian boson operators",
      "pseudo-hermitian boson annihilation operators",
      "standard hermite polynomials"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1185506,
      "adsabs": "2009arXiv0902.3744T"
    }
  }
}