{
  "id": "1801.02191",
  "version": "v1",
  "published": "2018-01-07T14:05:02.000Z",
  "updated": "2018-01-07T14:05:02.000Z",
  "title": "The hydrogen atom in $D=3-2ε$ dimensions",
  "authors": [
    "Gregory S. Adkins"
  ],
  "comment": "5 pages",
  "categories": [
    "quant-ph",
    "hep-ph"
  ],
  "abstract": "The nonrelativistic hydrogen atom in $D=3-2\\epsilon$ dimensions is the reference system for perturbative schemes used in dimensionally regularized nonrelativistic effective field theories to describe hydrogen-like atoms. Solutions to the $D$-dimensional Schr\\\"odinger-Coulomb equation are given in the form of a double power series. Energies and normalization integrals are obtained numerically and also perturbatively in terms of $\\epsilon$. The utility of the series expansion is demonstrated by the calculation of the divergent expectation value $\\langle (V')^2 \\rangle$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-07T14:05:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimensions",
      "divergent expectation value",
      "regularized nonrelativistic effective field theories",
      "nonrelativistic hydrogen atom",
      "series expansion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}