  The broadening of one-dimensional Gaussian wave packets is presented in all
textbooks on quantum mechanics. It is used to elucidate Heisenberg's
uncertainty relation. The behaviour on a lattice is drastically different if
the amplitude and/or phase of the wave packet varies on the scale of the
lattice constant. Important examples are very narrow wave packets ot wave
packets with an average velocity comparable to the maximum velocity on the
lattice. Analytical and numerical results for the time dependence of wave
packets on a one-dimensional lattice are presented.
