Energy levels and wave functions of electrons and holes in parabolic-quantum-well structures are calculated exactly by using the envelope-function approach and the usual connection rules. They show harmonic-oscillator-like behavior even under an electric field. Variational calculations are presented of the exciton binding energies and their Stark effect on the parabolic-quantum-well structures, which show stronger confinement than in a single rectangular quantum well.

• Received 27 January 1987

DOI:https://doi.org/10.1103/PhysRevB.37.1364