An intermediate-coupling exciton-phonon system allowing for the image potential in a polar semiconductor quantum well is studied for the first time. A double-time unitary transformation to the Hamiltonian of the system is carried out and the motion of the exciton in the z direction is studied in detail. The variation of the induced potential with the width of the well, the ground-state, and the first–excited-state energies of the exciton in the well for different widths of the well are calculated. The method used in this paper is suitable to both weak-coupling and intermediate-coupling exciton-phonon systems and the results are more accurate than those of a single-time unitary transformation which is only suitable to a weak-coupling exciton-phonon system.

• Received 9 January 1989

DOI:https://doi.org/10.1103/PhysRevB.40.9846