{
  "id": "1403.2824",
  "version": "v2",
  "published": "2014-03-12T06:26:48.000Z",
  "updated": "2014-05-01T14:07:30.000Z",
  "title": "Position-momentum uncertainty products",
  "authors": [
    "Zafar Ahmed",
    "Indresh Yadav"
  ],
  "comment": "Modified version, no Figures, one Table, 8 pages, to appear in Eur. J. Phys",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We point out two interesting features of position-momentum uncertainty product: $U=\\Delta x \\Delta p$. We show that two special (non-differentiable) eigenstates of the Schr{\\\"o}dinger operator with the Dirac Delta potential $[V(x)=-V_0 \\delta(x)],V_0>0$, also satisfy the Heisenberg's uncertainty principle by yielding $U> \\frac{\\hbar}{2}$. One of these eigenstates is a zero-energy and zero-curvature bound state.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-01T14:07:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "position-momentum uncertainty product",
      "dirac delta potential",
      "heisenbergs uncertainty principle",
      "zero-curvature bound state",
      "eigenstates"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0143-0807/35/4/045015",
      "journal": "European Journal of Physics",
      "year": 2014,
      "month": "Jul",
      "volume": 35,
      "number": 4,
      "pages": "045015"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014EJPh...35d5015A"
    }
  }
}