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arXiv · 1504.02509

A self-adjoint arrival time operator inspired by measurement models

J. J. Halliwell·J. Evaeus·J. London·Y. Malik
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Abstract

We introduce an arrival time operator which is self-adjoint and, unlike previously proposed arrival time operators, has a close link to simple measurement models. Its spectrum leads to an arrival time distribution which is a variant of the Kijowski distribution (a re-ordering of the current) in the large momentum regime but is proportional to the kinetic energy density in the small momentum regime, in agreement with measurement models. A brief derivation of the latter distribution is given. We make some simple observations about the physical reasons for self-adjointness, or its absence, in arrival time operators and in the momentum operator on the half-line and we also compare our operator with the dwell time operator.

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J. J. Halliwell, J. Evaeus, J. London, Y. Malik. 2015-07-08. A self-adjoint arrival time operator inspired by measurement models. https://doi.org/10.1016/j.physleta.2015.07.040

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