  We derive the expression for the energy uncertainty of the final state of a
decay of an unstable quantum state prepared at the initial time $t=0$. This
expression is function of the time $t$ at which a measurement is performed to
determine if the state has decayed and, if yes, in which one of the infinitely
many possible final states. For large times the energy spread is, as expected,
given by the decay width $\Gamma$ of the initial unstable state. However, if
the measurement of the final state is performed at a time $t$ comparable to (or
smaller than) the mean lifetime of the state $1/\Gamma$, then the uncertainty
on the energy of the final state is much larger than the decay width $\Gamma$.
Namely, for short times an uncertainty of the type $1/t$ dominates, while at
large times the usual spread $\Gamma$ is recovered. Then, we turn to a generic
two-body decay process and describe the energy uncertainty of each one of the
two outgoing particles. We apply these formulas to the two-body decays of the
neutral and charged pions and to the spontaneous emission process of an excited
atom. As a last step, we study a case in which the non-exponential decay is
realized ad show that for short times eventual asymmetric terms are enhanced in
the spectrum.
