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arXiv:1504.02509 · Physics Letters A

A self-adjoint arrival time operator inspired by measurement models

J. J. Halliwell, J. Evaeus, J. London, Y. Malik

Published Aug 1, 2015• 16 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2015.07.040

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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 1/2.1/2.1/2.