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APS » Journals » Phys. Rev. A » Volume 59 » Issue 3
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Phys. Rev. A 59, 1804–1808 (1999)

Time-of-arrival states

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J. Oppenheim1,*, B. Reznik2,†, and W. G. Unruh3,‡
1Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada V6T1Z1
2Theoretical Division, T-6, MS B288, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
3CIAR Gravity and Cosmology Program, Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada V6T1Z1

Received 17 July 1998; published in the issue dated March 1999

Although one can show formally that a time-of-arrival operator cannot exist, one can modify the low-momentum behavior of the operator slightly so that it is self-adjoint. We show that such a modification results in the difficulty that the eigenstates are drastically altered. In an eigenstate of the modified time-of-arrival operator, the particle, at the predicted time of arrival, is found far away from the point of arrival with probability 1/2.

© 1999 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.59.1804
DOI:
10.1103/PhysRevA.59.1804
PACS:
03.65.-w

*Electronic address: jono@physics.ubc.ca

†Electronic address: reznik@t6-serv.lanl.gov

‡Electronic address: unruh@physics.ubc.ca

 
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