  We present a computer simulation of exciton-exciton scattering in a quantum
well. Specifically, we use quantum Monte Carlo techniques to study the bound
and continuum states of two excitons in a 10 nm wide
GaAs/Al$_{0.3}$Ga$_{0.7}$As quantum well. From these bound and continuum states
we extract the momentum-dependent phase shifts for s-wave scattering. A
surprising finding of this work is that a commonly studied effective-mass mode
for excitons in a 10 nm quantum well actually supports two bound biexciton
states. The second, weakly bound state may dramatically enhance exciton-exciton
interactions. We also fit our results to a hard-disk model and indicate
directions for future work.
