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Quantum Physics

Title: Free motion time-of-arrival operator and probability distribution

Abstract: 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. {\bf 122}, 1649 (1961). We use Naimark's dilation theorem to reproduce the generalized decomposition of unity (or POVM) 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.
Comments: 10 a4 pages, no figures
Subjects: Quantum Physics (quant-ph)
Journal reference: Phys.Rev.A61:012104,1999
DOI: 10.1103/PhysRevA.61.012104
Report number: EHU-FT/9901
Cite as: arXiv:quant-ph/9905023
  (or arXiv:quant-ph/9905023v1 for this version)

Submission history

From: Inigo L. Egusquiza [view email]
[v1] Fri, 7 May 1999 14:30:19 GMT (18kb)