In Section 7.5.3 we defined the exciton creation operator c^†_k and the exciton– photon interaction

where a_k is the photon operator, and the constants in front of the sum are defined in Section 7.5.3.

Suppose that excitons exist in a semiconductor with energy gap h̄ω₀ and exciton binding energy Δ, and the initial state is an ensemble of single excitons with identical wave vector K(vector), and they have an average scattering time τ with phonons in the medium. Show that this system will yield a photon spectrum with a Lorentzian energy distribution, and determine the width of the Lorentzian.

V! int qN 2 Wk 2 EmVV mhao V wo (Pevaker + Pevack), k (8.4.15)