{
  "id": "0811.1222",
  "version": "v1",
  "published": "2008-11-07T21:06:38.000Z",
  "updated": "2008-11-07T21:06:38.000Z",
  "title": "Comparison theorems for the Klein-Gordon equation in d dimensions",
  "authors": [
    "Richard L. Hall",
    "M. D. S. Aliyu"
  ],
  "comment": "4 pages, 1 figure",
  "journal": "Phys. Rev. A 78, 052115 (2008)",
  "doi": "10.1103/PhysRevA.78.052115",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Two comparison theorems are established for discrete eigenvalues of the Klein-Gordon equation with an attractive central vector potential in d >= 1 dimensions. (I) If \\psi_1 and \\psi_2 are node-free ground states corresponding to positive energies E_1 >= 0 and E_2 >= 0, and V_1(r) <= V_2(r) <= 0, then it follows that E_1 <= E_2. (II) If V(r,a) depends on a parameter a \\in(a_1,a_2), V(r,a) <= 0, and E(a) is any positive eigenvalue, then \\partial V/\\partial a >= 0 ==> E'(a) >= 0 and \\partial V/\\partial a <= 0 ==> E'(a) <= 0.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-07T21:06:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Ge",
      "03.65.Pm"
    ],
    "keywords": [
      "klein-gordon equation",
      "comparison theorems",
      "dimensions",
      "attractive central vector potential",
      "discrete eigenvalues"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2008,
      "month": "Nov",
      "volume": 78,
      "number": 5,
      "pages": "052115"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008PhRvA..78e2115H"
    }
  }
}