{
  "id": "2211.14724",
  "version": "v1",
  "published": "2022-11-27T04:59:57.000Z",
  "updated": "2022-11-27T04:59:57.000Z",
  "title": "On the experimental verification of the uncertainty principle of position and momentum",
  "authors": [
    "Thomas Schürmann",
    "Ingo Hoffmann",
    "Winfrid Görlich"
  ],
  "categories": [
    "quant-ph"
  ],
  "abstract": "Historically, Kennard was the first to choose the standard deviation as a quantitative measure of uncertainty, and neither he nor Heisenberg explicitly explained why this choice should be appropriate from the experimental physical point of view. If a particle is prepared by a single slit of spatial width $\\Delta x$, it has been shown that a finite standard deviation $\\sigma_p<\\infty$ can only be ensured if the wave-function is zero at the edge of $\\Delta x$, otherwise it does not exist. Under this circumstances the corresponding sharp inequality is $\\sigma_p\\Delta x\\geq \\pi\\hbar$. This bound will be reconsidered from the mathematical point of view in terms of a variational problem in Hilbert space and will furthermore be tested in a 4f-single slit diffraction experiment of a laser beam. Our results will be compared with a laser-experiment recently given by M. F. Guasti (2022).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-27T04:59:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uncertainty principle",
      "experimental verification",
      "4f-single slit diffraction experiment",
      "finite standard deviation",
      "laser beam"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}