  The phenomenon of wave packet diffraction in space and time is described. It
consists in a diffraction pattern whose spatial location progresses with time.
The pattern is produced by wave packet quantum scattering off an attractive or
repulsive time independent potential. An analytical formula for the pattern at
$t\to\infty$ is derived both in one dimension and in three dimensions. The
condition for the pattern to exist is developed. The phenomenon is shown
numerically and analytically for the Dirac equation in one dimension also. An
experiment for the verification of the phenomenon is described and simulated
numerically.
