  The split-operator technique for wave packet propagation in quantum systems
is expanded here to the case of propagating wave functions describing
Schr\"odinger particles, namely, charge carriers in semiconductor
nanostructures within the effective mass approximation, in the presence of
Zeeman effect, as well as of Rashba and Dresselhaus spin-orbit interactions. We
also demonstrate that simple modifications to the expanded technique allow us
to calculate the time evolution of wave packets describing Dirac particles,
which are relevant for the study of transport properties in graphene.
