We remark that the often ignored quantum probability current is fundamental
for a genuine understanding of scattering phenomena and, in particular, for the
statistics of the time and position of the first exit of a quantum particle
from a given region, which may be simply expressed in terms of the current.
This simple formula for these statistics does not appear as such in the
literature. It is proposed that the formula, which is very different from the
usual quantum mechanical measurement formulas, be verified experimentally. A
full understanding of the quantum current and the associated formula is
provided by Bohmian mechanics.Comment: 15 pages, 3 figures, revised and more detailed version, to be
published in Journal of Statistical Physics, August 9