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Measurement of Time-of-Arrival in Quantum Mechanics

Aharonov, Y.; Oppenheim, J.; Popescu, Sandu; Reznik, Benni; Unruh, W.G.

HPL-BRIMS-97-22

Keyword(s): quantum mechanics; time of arrival; measurement theory

Abstract: It is argued that the time-of-arrival cannot be precisely defined and measured in quantum mechanics. By constructing explicit toy models of a measurement, we show that for a free particle it cannot be measured more accurately than ?tA ~ ? / Ek, where Ek is the initial kinetic energy of the particle. With a better accuracy, particles reflect off the measuring device, and the resulting probability distribution becomes distorted. It is shown that the measurements considered here do not correspond to a measurement of the time-of-arrival operator.

27 Pages

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