Arrival time in quantum mechanics

Arrival Time in Quantum Mechanics

Time of arrival in quantum mechanics.

We study the problem of computing the probability for the time-of-arrival of a quantum particle at a given spatial position. We consider a solution to this problem based on the spectral decomposition of the particle's (Heisenberg) state into the eigenstates of a suitable operator, which we denote as the \time-of-arrival" operator. We discuss the general properties of this operator. We construct...

Measurement of time of arrival in quantum mechanics

Y. Aharonov, J. Oppenheim,* S. Popescu, B. Reznik, and W. G. Unruh School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel and Department of Physics, University of South Carolina, Columbia, South Carolina 29208 Department of Physics, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia, Canada V6T 1Z1 Isaac Newton Institute, Cambridge Universi...

Time of arrival in Classical and Quantum Mechanics

The time of arrival at an arbitrary position in configuration space can be given as a function of the phase space variables for the Liouville integrable systems of classical mechanics, but only for them. We review the Jacobi-Lie transformation that explicitly implements this function of positions and momenta. We then discuss the recently developed quantum formalism for the time of arrival. We f...

Probability distribution of arrival times in quantum mechanics

In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)] we introduced a self-adjoint operator T̂ (X) whose eigenstates can be used to define consistently a probability distribution of the time of arrival at a given spatial point. In the present work we show that the probability distribution previously proposed can be well understood on classical grounds in the sense that it...