Electronic excitation by short x-ray pulses: from quantum beats to wave packet revivals

We propose a simple way to determine the periodicities of wave packets (WPs) in quantum systems directly from the energy differences of the states involved. The resulting classical periods and revival times are more accurate than those obtained with the traditional expansion of the energies about the central quantum number , especially when is low. The latter type of WP motion occurs upon excitation of highly charged ions with short XUV or x-ray pulses. Moreover, we formulate the WP dynamics in such a form that it directly reveals the origin of phase shifts in the maxima of the autocorrelation function, a phenomenon most prominent in the low WP dynamics.