Arrival and departure time in quantum mechanics

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Abstract
The arrival time at a point in the case of the one-dimensional motion of a classical particle is only predictable if initially the position and velocity are both known precisely. It is shown that such an arrival time can be defined in a probabilistic sense when only the initial means and standard deviations of position and velocity are known. The arrival time so defined depends on the subjective concept of confidence limit. It is further shown that arrival time in the latter sense goes over to quantum mechanics. A lower bound on the transit time is derived for this situation by use of the Mandelstam-Tamm inequality.