  In this paper we discuss some aspects of the theory of wave packets. We
consider a popular non-covariant Gaussian model used in various applications
and show that it predicts too slow a longitudinal dispersion rate for
relativistic particles. We revise this approach by considering a covariant
model of Gaussian wave packets, and examine our results by inspecting a wave
packet of arbitrary form. A general formula for the time dependence of the
dispersion of a wave packet of arbitrary form is found. Finally, we give a
transparent interpretation of the disappearance of the wave function over time
due to the dispersion --- a feature often considered undesirable, but which is
unavoidable for wave packets. We find, starting from simple examples,
proceeding with their generalizations and finally by considering the continuity
equation, that the integral over time of both the flux and probability
densities are asymptotically proportional to the factor 1/L^2 in the rest frame
of the wave packet, just as in the case of an ensemble of classical particles.
