{
  "id": "quant-ph/0210106",
  "version": "v1",
  "published": "2002-10-14T09:59:41.000Z",
  "updated": "2002-10-14T09:59:41.000Z",
  "title": "Universal Formula for the Expectation Value of the Radial Operator under the Aharonov-Bohm Flux and the Coulomb Field",
  "authors": [
    "W. F. Kao",
    "Y. M. Kao",
    "D. H. Lin"
  ],
  "comment": "11 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "A useful and universal formula for the expectation value of the radial operator in the presence of the Aharonov-Bohm flux and the Coulomb Field is established. We find that the expectation value $< r^{\\lambda}>$ $(-\\infty \\leq \\lambda \\leq \\infty)$ is greatly affected due to the non-local effect of the magnetic flux although the Aharonov-Bohm flux does not have any dynamical significance in classical mechanics. In particular, the quantum fluctuation increases in the presence of the magnetic flux due to the Aharonov-Bohm effect. In addition, the Virial theory in quantum mechanics is also constructed for the spherically symmetric system under the Aharonov-Bohm effect.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-14T09:59:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "expectation value",
      "aharonov-bohm flux",
      "radial operator",
      "coulomb field",
      "universal formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002quant.ph.10106K"
    }
  }
}