Ionization for Three Dimensional Time-Dependent Point Interactions

We study the time evolution of a three dimensional quantum particle under the action of a time-dependent point interaction fixed at the origin.We assume that the “strength” of the interaction α(t) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of α(t), we prove that there is complete ionization as t →∞, starting from a bound state at time t = 0. Moreover we prove also that, under the same conditions, all the states of the system are scattering states.