2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95957We 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 \to \infty), 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.Some improvements and some references added, 26 pages, LaTeXMathematical PhysicsQuantum Physicstext