Measurement of Time-of-Arrival in Quantum Mechanics

Details Measurement of Time-of-Arrival in Quantum Mechanics Measurement of Time-of-Arrival in Quantum Mechanics

1997-09-14

arxiv.org/abs/quant-ph/9709031v3

Phys.Rev. A57 (1998) 4130

Physics

Quantum Physics

References added. To appear in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.57.4130

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 then $\Delta t_A \sim 1/E_k$, where $E_k$ 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 a time-of-arrival operator cannot exist, and that approximate time-of-arrival operators do not correspond to the measurements considered here.

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