M. Correggi, G.F. Dell'Antonio, R. Figari, A. Mantile
Ionization for Three Dimensional Time-dependent Point Interactions
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ABSTRACT. 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 \( \alpha(t) \) is a periodic function with an arbitrary mean. Under very weak conditions on the Fourier coefficients of \( \alpha(t) \), we prove that there is complete ionization as \( t \rightarrow \infty \), 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.