  Gaussian wave packets (GWPs) are well suited as basis functions to describe
the time evolution of arbitrary wave functions in systems with nonsingular
smooth potentials. They are less so in atomic systems on account of the
singular behavior of the Coulomb potential. We present a time-dependent
variational method that makes the use of GWPs possible in the description of
propagation of quantum states also in these systems. We do so by a
regularization of the Coulomb potential, and by introduction of a fictitious
time coordinate in which the evolution of an initial state can be calculated
exactly and analytically for a pure Coulomb potential. Therefore in perturbed
atomic systems variational approximations only arise from those parts of the
potentials which deviate from the Coulomb potential. The method is applied to
the hydrogen atom in external magnetic and electric fields. It can be adapted
to systems with definite symmetries, and thus allows for a wide range of
applications.
