DIFFRACTION IN TIME IN A KRONIG-PENNEY LATTICE

The transient behavior of wave packets of electrons in crystals may po ssibly be accessible to experiments with present techniques. Thus it i s interesting to study this problem theoretically. The simplest exampl e is a Kronig-Penney lattice, with delta function potentials, and with a wave packet in one of its segments. We study the behavior of this p acket as function of time t if the position x is fixed or vice versa, and derive the general characteristics of the phenomena. In particular we compare our results with the diffraction in time behavior studied long ago by one of the authors (M.M.) when the potential vanish, i.e. for the free packet. It is shown that the characteristic oscillations of the diffraction in time can also appear in the Kronig-Penney lattic e. In addition, we have observed that the situation when the energy of the initial state of the particles lies within the bands is essential ly indistinguishable from that where it lies within the gaps. The conn ection with the nonrelativistic diffusion problem in quantum mechanics is also briefly discussed.