{
  "id": "quant-ph/9603021",
  "version": "v1",
  "published": "1996-03-14T16:16:32.000Z",
  "updated": "1996-03-14T16:16:32.000Z",
  "title": "Time-of-arrival in quantum mechanics",
  "authors": [
    "Norbert Grot",
    "Carlo Rovelli",
    "Ranjeet S. Tate"
  ],
  "comment": "Latex/Revtex, 20 pages. 2 figs included using epsf. Submitted to Phys. Rev. A",
  "journal": "Phys.Rev. A54 (1996) 4679",
  "doi": "10.1103/PhysRevA.54.4676",
  "categories": [
    "quant-ph",
    "gr-qc"
  ],
  "abstract": "We study the problem of computing the probability for the time-of-arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle's (Heisenberg) state into the eigenstates of a suitable operator, which we denote as the ``time-of-arrival'' operator. We discuss the general properties of this operator. We construct the operator explicitly in the simple case of a free nonrelativistic particle, and compare the probabilities it yields with the ones estimated indirectly in terms of the flux of the Schr\\\"odinger current. We derive a well defined uncertainty relation between time-of-arrival and energy; this result shows that the well known arguments against the existence of such a relation can be circumvented. Finally, we define a ``time-representation'' of the quantum mechanics of a free particle, in which the time-of-arrival is diagonal. Our results suggest that, contrary to what is commonly assumed, quantum mechanics exhibits a hidden equivalence between independent (time) and dependent (position) variables, analogous to the one revealed by the parametrized formalism in classical mechanics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-03-14T16:16:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum mechanics",
      "time-of-arrival",
      "free nonrelativistic particle",
      "quantum particle",
      "spectral decomposition"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. A"
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 416762
    }
  }
}