Reflection-free propagation of wave packets

We analyze the problem of suppression of reflections within the numerical propagation of wave packets using finite atomiclike pseudostate expansions. Artificial reflections at effective “walls” and reentering of probability flux into the interaction region represents a major limitation for the study of long-time evolution of atomic ionization processes. We propose two methods, the repetitive projection method (RPM) and Siegert pseudostate (SPS) propagation, and study their efficiency in suppressing reflections. It is shown that the quantum Zeno effect sets a limit on the efficiency of the RPM as well as of masking functions. For the exactly solvable propagation of a radial-free wave packet, we show that both the SPS and the RPM provide almost complete suppression of reflections without appreciable distortion in the physically relevant region of coordinate space.