Nonperturbative Time Dependent Solution of a Simple Ionization Model

We present a non-perturbative solution of the Schrödinger equation iψt = −ψxx−(2−α sinωt)δ(x)ψ describing the ionization of a model atom by a parametric oscillating potential. This model has been studied extensively by many authors, including us. It has surprisingly many features in common with those observed in the ionization of real atoms and emission by solids, subjected to microwave or laser radiation. Here we go beyond previous investigations in providing complete mathematical proofs for the full time evolution for all values of α and ω using novel compact operator and analytic tools. This includes the energy distribution of the emitted electrons, not studied previously for this model. We expect that this will serve as a basis for treating more realistic systems revealing a form of universality in di erent emission processes.