{
  "id": "math-ph/0512079",
  "version": "v1",
  "published": "2005-12-22T16:46:19.000Z",
  "updated": "2005-12-22T16:46:19.000Z",
  "title": "Exact solutions for semirelativistic problems with non-local potentials",
  "authors": [
    "Richard L. Hall"
  ],
  "comment": "13 pages, 3 figures",
  "journal": "J. Phys. A 39, 903 - 912 (2006)",
  "doi": "10.1088/0305-4470/39/4/011",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "It is shown that exact solutions may be found for the energy eigenvalue problem generated by the class of semirelativistic Hamiltonians of the form H = sqrt{m^2+p^2} + hat{V}, where hat{V} is a non-local potential with a separable kernel of the form V(r,r') = - sum_{i=1}^n v_i f_i(r)g_i(r'). Explicit examples in one and three dimensions are discussed, including the Yamaguchi and Gauss potentials. The results are used to obtain lower bounds for the energy of the corresponding N-boson problem, with upper bounds provided by the use of a Gaussian trial function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-22T16:46:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exact solutions",
      "non-local potential",
      "semirelativistic problems",
      "gaussian trial function",
      "semirelativistic hamiltonians"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}