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.
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