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 Schrödinger 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.

15 pages, 3 figures