  Wave functions of heavy-hole excitons in GaAs/Al$_{0.3}$Ga$_{0.7}$As square
quantum wells (QWs) of various widths are calculated by the direct numerical
solution of a three-dimensional Schr\"odinger equation using a
finite-difference scheme. These wave functions are then used to determine the
exciton-exciton, exciton-electron and exciton-hole fermion exchange constants
in a wide range of QW widths (5-150 nm). Additionally, the spin-dependent
matrix elements of elastic exciton-exciton, exciton-electron and exciton-hole
scattering are calculated. From these matrix elements, the collisional
broadening of the exciton resonance is obtained within the Born approximation
as a function of the areal density of excitons, electrons and holes
respectively for QW widths of 5, 15, 30 and 50 nm. The obtained numerical
results are compared with other theoretical works.
