Quantile Motion in One Dimension
In classical mechanics the position x(t) of a point particle and its velocity v(t) = dx(t)/dt 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)〉/dt 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 dx P (t)/dt 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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