## Abstract

In classical mechanics the position *x*(*t*) of a point particle and its velocity *v*(*t*) = dx(*t*)/d*t* are well defined. This is not the case in quantum mechanics. For a free wave packet one can use the expectation value 〈*x*(*t*)〉 and its time derivative d〈*x*(*t*)〉/d*t* to characterize the position and the velocity of a particle. But for a particle under the influence of a force this description is not adequate. In the case of the tunnel effect, for instance, the expectation value 〈*x*(*t*)〉 may never pass through the barrier. In the following we shall see that mathematical statistics allows us to define a quantile position *x*_{ P }(*t*) and a quantile velocity d*x*_{ P }(*t*)/d*t* in all cases where we deal with a probability distribution *ϱ*(*x*,*t*) and that this velocity can be related to experiment. (This chapter and Section 10.2 are based on the following publication: S. Brandt, H.D. Dahmen, E. Gjonaj, T. Stroh, Physics Letters A 249, 265 (1998).)

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