{
  "id": "1002.3005",
  "version": "v2",
  "published": "2010-02-16T05:45:05.000Z",
  "updated": "2010-02-26T16:54:19.000Z",
  "title": "Position Uncertainty in the Heisenberg Uncertainty Relation",
  "authors": [
    "Seiji Kosugi"
  ],
  "comment": "Corrected typos. 18 pages, to be published in Prog. Theor. Phys.",
  "journal": "Prog. Theor, Phys. 123 (2010) 431-448",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Position measurements are examined under the assumption that object position x_t and probe position X_t just after the measurement are expressed by a linear combination of positions x_0 and X_0 just before the measurement. The Heisenberg uncertainty relation between the position uncertainty and momentum disturbance holds when the measurement error \\epsilon(x_t) for the object position x_t is adopted as the position uncertainty. However, the uncertainty in the measurement result obtained for x_0 is the standard deviation of the measurement result, and not the measurement error \\epsilon(x_0). This difference is due to the reduction of a wave packet. The validity of the linearity assumption is examined in detail.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-02-26T16:54:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heisenberg uncertainty relation",
      "position uncertainty",
      "object position",
      "measurement result",
      "measurement error"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Progress of Theoretical Physics",
      "year": 2010,
      "month": "Mar",
      "volume": 123,
      "number": 3,
      "pages": 431
    },
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010PThPh.123..431K"
    }
  }
}