  We show how to compute the optical functions of Wide Parabolic Quantum Wells
(WPQWs) exposed to uniform electric F applied in the growth direction, in the
excitonic energy region. The effect of the coherence between the electron-hole
pair and the electromagnetic field of the propagating wave including the
electron-hole screened Coulomb potential is adopted, and the valence band
structure is taken into account in the cylindrical approximation. The role of
the interaction potential and of the applied electric field, which mix the
energy states according to different quantum numbers and create symmetry
forbidden transitions, is stressed. We use the Real Density Matrix Approach
(RDMA) and an effective e-h potential, which enable to derive analytical
expressions for the WPQWs electrooptical functions. Choosing the
susceptibility, we performed numerical calculations appropriate to a
GaAs/GaAlAs WPQWs. We have obtained a red shift of the absorption maxima
(Quantum Confined Stark Effect), asymmetric upon the change of the direction of
the applied field (F -> -F), parabolic for the ground state and strongly
dependent on the confinement parameters (the QWs sizes), changes in the
oscillator strengths, and new peaks related to the states with different parity
for electron and hole.
