The exciton wavefunction in parabolic quantum wells is calculated usin
g variational techniques and effective mass theory. The influences of
the potential shape and of confinement on the exciton binding energies
are studied. The results are in good agreement with previous calculat
ions. The oscillator-strength of excitons in GaAs/Ga1-xAlxAs quantum w
ells has a maximum value very close to the cross-over from three to tw
o dimensions.