  We study the time evolution of the wave function of a particle bound by an
attractive $\delta$-function potential when it is subjected to time dependent
variations of the binding strength (parametric excitation). The simplicity of
this model permits certain nonperturbative calculations to be carried out
analytically both in one and three dimensions. Thus the survival probability of
bound state $|\theta(t)|^2$, following a pulse of strength $r$ and duration
$t$, behaves as $|\theta(t)|^2 -|\theta(\infty)|^2 \sim t^{-\alpha}$, with both
$\theta(\infty)$ and $\alpha$ depending on $r$. On the other hand a sequence of
strong short pulses produces an exponential decay over an intermediate time
scale.
