  We present a nonrelativistic theory for the quantum mechanical description of
longitudinal atomic beam spin echo experiments, where a beam of neutral atoms
is subjected to static electric and magnetic fields. The atomic wave function
is the solution of a matrix-valued Schroedinger equation and can be written as
superposition of local (atomic) eigenstates of the potential matrix. The
position- and time-dependent amplitude function of each eigenstate represents
an atomic wave packet and can be calculated in a series expansion with a master
formula that we derive. The zeroth order of this series expansion describes the
adiabatic limit, whereas the higher order contributions contain the mixing of
the eigenstates and the corresponding amplitude functions.
  We give a tutorial for the theoretical description of longitudinal atomic
beam spin echo experiments and for the so-called Fahrplan model, which is a
visualisation tool for the propagation of wave packets of different atomic
eigenstates.
  As an example for the application of our theory, we study parity violating
geometric (Berry-)phases. In this context, we define geometric flux densities,
which for certain field configurations can be used to illustrate geometric
phases in a vector diagram. Considering an example with a specific field
configuration, we prove the existence of a parity violating geometric phase.
