{
  "id": "1407.6170",
  "version": "v3",
  "published": "2014-07-23T10:55:28.000Z",
  "updated": "2014-12-11T10:14:00.000Z",
  "title": "Quantum propagator and characteristic equation in the presence of a chain of $δ$-potentials",
  "authors": [
    "A. Refaei",
    "F. Kheirandish"
  ],
  "comment": "15 pages, 2 figures",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "The quantum propagator and characteristic equation in the presence of a chain of $\\delta$-potentials are obtained in the rectangular, cylindrical and spherical coordinate systems. The simplicity and efficiency of the method is illustrated via examples. As an application, the characteristic equation of a quantum harmonic oscillator confined to an infinite box is obtained. The roots of the characteristic equation, determining the energy eigenvalues of the restricted oscillator, are calculated approximately and compared with the existing numerical data.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-27T00:45:58.000Z",
      "title": "On $δ$-potential Green's functions and their applications",
      "abstract": "The method introduced in \\cite{main} to obtain the Green's function in the presence of a $\\delta$-potential, is generalized to the case of a combination of delta-potentials with different strength parameters in rectangular, cylindrical and spherical coordinate systems. Closed analytic representations of the Green's function are given for arbitrary number of $\\delta$-functions. Five examples are given to illustrate the simplicity and efficiency of the method. The application of the method to confinement problems is investigated trough examples. Characteristic equations for determining the energy eigenvalues in confinement cases are obtained, in particular a characteristic equation for a quantum harmonic oscillator confined to an infinite box is given and its roots are calculated approximately and compared with the reported data \\cite{Aguilera}.",
      "comment": "(Extended)",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2014-12-11T10:14:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.-w",
      "03.65.Fd",
      "03.65.Ge"
    ],
    "keywords": [
      "potential greens functions",
      "application",
      "characteristic equation",
      "quantum harmonic oscillator",
      "trough examples"
    ],
    "publication": {
      "doi": "10.1142/S021797921550099X",
      "journal": "International Journal of Modern Physics B",
      "year": 2015,
      "month": "Apr",
      "volume": 29,
      "number": 15,
      "pages": 1550099
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015IJMPB..2950099R"
    }
  }
}