Excitons in coupled quantum wells open the possibility to reach high densities close to equilibrium. In a recent experiment employing a lateral trap potential, a blue shift and a broadening of the exciton emission line has been seen (Snoke, SSC 134). The standard Hartree-Fock treatment can explain the blue shift but fails to give a finite broadening. Starting from the (spin-dependent) many-exciton Hamiltonian with direct and exchange potential, we present a dynamical T-matrix calculation for the single-exciton Greens function which is directly related to the frequency- and angle-resolved photoluminescence. The calculated spectrum is blue shifted and broadened due to exciton-exciton scattering. At high excitation, both the spectrum and the angular emission are getting narrow. This is a direct manifestation for off-diagonal long range order and a precursor of condensation.
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