A self-adjoint arrival time operator inspired by measurement models

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.

20 pages, Latex. Imperial College preprint. Substantially expanded

References in corpus (4)

• The Quantum Mellin transform
• Disclosing hidden information in the quantum Zeno effect: Pulsed measurement of the quantum time of arrival
• Relation between quantum dwell times and flux-flux correlations
• Optimal Covariant Measurement of Momentum on a Half Line in Quantum Mechanics

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• Space-time symmetric extension of non-relativistic quantum mechanics
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• The time distribution of quantum events
• Does the Heisenberg uncertainty principle apply along the time dimension?
• Quantum nature of time -- proposition of experimental verification