{
  "id": "quant-ph/0009046",
  "version": "v2",
  "published": "2000-09-11T16:05:52.000Z",
  "updated": "2001-06-19T13:17:58.000Z",
  "title": "On the connection between the radial momentum operator and the Hamiltonian in n dimensions",
  "authors": [
    "Gil Paz"
  ],
  "comment": "Some text and several references added, to appear in the European Journal of Physics",
  "journal": "European Journal of Physics Vol. 22 no. 4 p. 337",
  "doi": "10.1088/0143-0807/22/4/308",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The radial momentum operator in quantum mechanics is usually obtained through canonical quantization of the (symmetrical form of the) classical radial momentum. We show that the well known connection between the Hamiltonian of a free particle and the radial momentum operator $\\hat{H}=\\hat{P}_{r}^2/2m+ $\\hat{L}^2$}/2mr^{2}$ is true only in one or three dimensions. In general, an extra term of the form $\\hbar^{2}(n-1)(n-3)/ 2m \\cdot 4r^{2}$ has to be added to the Hamiltonian.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-06-19T13:17:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "radial momentum operator",
      "hamiltonian",
      "dimensions",
      "connection",
      "quantum mechanics"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}