  We model the effects of cross-phase modulation in frequency (or wavelength)
division multiplexed optical communications systems, using a Schr\"odinger
equation with a spatially and temporally random potential. Green's functions
for the propagation of light in this system are calculated using Feynman
path-integral and diagrammatic techniques. This propagation leads to a
non-Gaussian joint distribution of the input and output optical fields. We use
these results to determine the amplitude and timing jitter of a signal pulse
and to estimate the system capacity in analog communication.
