  We present a detailed non-perturbative analysis of the time-evolution of a
well-known quantum-mechanical system - a particle between potential walls -
describing the decay of unstable states. For sufficiently high barriers,
corresponding to unstable particles with large lifetimes, we find an
exponential decay for intermediate times, turning into an asymptotic power
decay. We explicitly compute such power terms in time as a function of the
coupling in the model. The same behavior is obtained with a repulsive as well
as with an attractive potential, the latter case not being related to any
tunnelling effect.
