On the complete ionization of a periodically perturbed quantum system

TL;DR

This paper demonstrates that a one-dimensional quantum system with a zero-range potential becomes fully ionized over time when subjected to a periodic parametric perturbation of any strength and frequency.

Contribution

It provides a rigorous proof that such quantum systems inevitably lose their bound states under periodic perturbations, leading to complete ionization.

Findings

Wave function projection on bound state vanishes over time

System becomes fully ionized as time approaches infinity

Ionization occurs regardless of perturbation strength and frequency

Abstract

We analyze the time evolution of a one-dimensional quantum system with zero range potential under time periodic parametric perturbation of arbitrary strength and frequency. We show that the projection of the wave function on the bound state vanishes, i.e. the system gets fully ionized, as time grows indefinitely.