  We discuss the relation between the quantum-mechanical survival probability
of an unstable system in motion and that of the system at rest. The usual
definition of the survival probability which takes into account only the time
evolution of an unstable system leads to a relation between the survival
probability of the system in motion and that of the system at rest which is
different from the standard relation based on relativistic time dilation. This
approach led other authors to claim non-standard quantum-mechanical effects
which are in clear contradiction with Special Relativity. We show that an
appropriate relativistic definition of the survival probability which takes
into account also the space evolution of an unstable system leads to the
standard relation between the survival probability of the system in motion and
that of the system at rest, in agreement with Special Relativity. We present a
rigorous derivation of this result based on a wave packet treatment.
