{
  "id": "1007.4243",
  "version": "v2",
  "published": "2010-07-24T04:00:47.000Z",
  "updated": "2011-03-18T15:20:51.000Z",
  "title": "Quantum mechanics of a free particle from properties of the Dirac delta function",
  "authors": [
    "Denys I. Bondar",
    "Robert R. Lompay",
    "Wing-Ki Liu"
  ],
  "comment": "3 pages",
  "journal": "American Journal of Physics 79: 392 (2011)",
  "doi": "10.1119/1.3533715",
  "categories": [
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "Based on the assumption that the probability density of finding a free particle is independent of position, we infer the form of the eigenfunction for the free particle, $\\bra{x} p > = \\exp(ipx/\\hbar)/\\sqrt{2\\pi\\hbar}$. The canonical commutation relation between the momentum and position operators and the Ehrenfest theorem in the free particle case are derived solely from differentiation of the delta function and the form of $\\bra{x} p >$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-18T15:20:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.-w"
    ],
    "keywords": [
      "dirac delta function",
      "quantum mechanics",
      "properties",
      "free particle case",
      "probability density"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "American Journal of Physics",
      "year": 2011,
      "month": "Apr",
      "volume": 79,
      "number": 4,
      "pages": 392
    },
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011AmJPh..79..392B"
    }
  }
}