{
  "id": "1510.01138",
  "version": "v1",
  "published": "2015-10-05T13:17:51.000Z",
  "updated": "2015-10-05T13:17:51.000Z",
  "title": "The Coulomb potential V(r)=1/r and other radial problems on the Bethe lattice",
  "authors": [
    "Olga Petrova",
    "Roderich Moessner"
  ],
  "comment": "5 pages + references",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the problem of a particle hopping on the Bethe lattice in the presence of a Coulomb potential. We obtain an exact solution to the particle's Green's function along with the full energy spectrum. In addition, we present a mapping of a generalized radial potential problem defined on the Bethe lattice to an infinite number of one dimensional problems that are easily accessible numerically. The latter method is particularly useful when the problem admits no analytical solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-05T13:17:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bethe lattice",
      "coulomb potential",
      "radial problems",
      "particles greens function",
      "full energy spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}