  We study the effect of quantum motion in a Mach-Zehnder interferometer where
ultracold, two-level atoms cross a $\pi/2 $-$\pi $-$\pi/2$ configuration of
separated, laser illuminated regions. Explicit and exact expressions are
obtained for transmission amplitudes of monochromatic, incident atomic waves
using recurrence relations which take into account all possible paths: the
direct ones usually considered in the simple semiclassical treatment, but
including quantum motion corrections, and the paths in which the atoms are
repeatedly reflected at the fields.
