Numerical approach to solve the time-dependent Dirac equation

We discuss how split-operator techniques may be applied to calculate normalized wave-function solutions to the three-dimensional time-dependent Dirac equation on a space-time lattice grid. This approach can be used to investigate various field-free dynamics of electron wave packets as well as the interactions of atomic electrons with space-time varying electromagnetic radiation. We demonstrate this technique by analyzing the time-resolved Klein paradox and the Zitterbewegung.