  We present a simplified model for dynamical diffraction of particles through
a periodic thick perfect crystal based on repeated application of a coherent
beam splitting unitary at coarse-grained lattice sites. By demanding
translational invariance and a computationally tractable number of sites in the
coarse-graining we show how this approach reproduces many results typical of
dynamical diffraction theory and experiments. This approach has the benefit of
being applicable in the thick, thin, and intermediate crystal regimes. The
method is applied to a three-blade neutron interferometer to predict the output
beam profiles, interference patterns, and contrast variation.
