Phys. Rev. A 61, 012104 (1999) [9 pages]Free-motion time-of-arrival operator and probability distributionSee Also: Erratum Received 7 May 1999; published 9 December 1999 We reappraise and clarify the contradictory statements found in the literature concerning the time-of-arrival operator introduced by Aharonov and Bohm in Phys. Rev. 122, 1649 (1961). We use Naimark’s dilation theorem to reproduce the generalized decomposition of unity (or positive-operator-valued measures) from any self-adjoint extension of the operator, emphasizing a natural one, which arises from the analogy with the momentum operator on the half-line. General time operators are set within a unifying perspective. It is shown that they are not in general related to the time of arrival, even though they may have the same form. © 1999 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevA.61.012104
DOI:
10.1103/PhysRevA.61.012104
PACS:
03.65.-w
See AlsoErratum: I. L. Egusquiza and J. G. Muga, Erratum: Free-motion time-of-arrival operator and probability distribution [Phys. Rev. A 61, 012104 (2000)], Phys. Rev. A 61, 059901 (2000). |
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