Abstract
A new implementation of the split-operator method for calculating the time-evolution of Dirac wave functions is presented. With the help of self-adaptive numerical grids we are able to study the dynamics of an initially free electronic Dirac wave packet under the influence of an ultra-intense laser pulse and its scattering at a highly charged ion. Furthermore, we provide the necessary tools for constructing the Dirac ground state wave function of any single-electron ion and demonstrate them for hydrogenic oxygen. Bound Dirac dynamics in a super-strong laser field is finally investigated.
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