The exciton-exciton interaction is investigated for quasi-two-dimensional quantum structures. A bosonization scheme is applied including the full spin structure. For generating the effective interaction potentials, the Hartree-Fock and Heitler-London approaches are improved by a full twoexciton calculation which includes the van der Waals effect. With these potentials the biexciton formation in bilayer systems is investigated. For coupled quantum wells the two-body scattering matrix is calculated and employed to give a modified relation between exciton density and blueshift. Such a relation is of central importance for gauging exciton densities in experiments which pave the way toward Bose-Einstein condensation of excitons.

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The coherent-potential approximation (CPA) is extended to describe satisfactorily the motion of particles in a random potential which is spatially correlated and smoothly varying. In contrast to existing cluster-CPA methods, the present scheme preserves the simplicity of the conventional CPA but leads to a momentum and frequency-dependent self-energy. Its accuracy is checked by a comparison with the exact moments of the Green's function, and with the spectral function from numerical simulations. The scheme is applied to excitonic absorption spectra in different spatial dimensions.