Rearrangement of a wave packet interacting with a semi-bounded medium

The calculation of the density matrix of a particle interacting with a semi-bounded medium makes it possible to investigate the rearrangement of a wide (compared with the interatomic distance) wave packet for a particle not only approaching the surface but also penetrating into the medium. It is shown that the entry of the particle into the volume of the medium is accompanied by rearrangement of the wave packet into a statistical ensemble of narrow packets, whose widths decrease with the time in accordance with the law $\sim t^{-1/2}$.