We present a simple method to compute the optical properties of quantu
m wells of any shape, using microscopic calculations of the electronic
states. Near the exciton resonances simple expressions for the polari
ton states and the radiative lifetimes are obtained as functions of th
e in-plane wave vector K-I. The cases of a GaAs/AlxGa1-xAs/AlAs asymme
tric well and of double wells are considered; the results relate to th
ose of the symmetric well. The computed splitting between the Z mode a
nd the T mode is shown to depend mostly on the thickness, in fair agre
ement with experiments by Frohlich ef al. Polaritons associated with c
rossed excitons involving pairs of subbands forbidden in the symmetric
case are found, and are shown to give rise to additional structure in
the reflectivity.