  We study the transition to the continuum of an initially bound quantum
particle in $\RR^d$, $d=1,2,3$, subjected, for $t\ge 0$, to a time periodic
forcing of arbitrary magnitude. The analysis is carried out for compactly
supported potentials, satisfying certain auxiliary conditions. It provides
complete analytic information on the time Laplace transform of the wave
function. From this, comprehensive time asymptotic properties (Borel summable
transseries) follow. We obtain in particular a criterion for whether the wave
function gets fully delocalized (complete ionization). This criterion shows
that complete ionization is generic and provides a convenient test for
particular cases. When satisfied it implies absence of discrete spectrum and
resonances of the associated Floquet operator. As an illustration we show that
the parametric harmonic perturbation of a potential chosen to be any nonzero
multiple of the characteristic function of a measurable compact set has this
property.
