Exciton Theory by Second Quantization

Agranovich's solution of the molecular exciton problem, in which the representation of second quantization is used, was outlined. The assumptions of the theory, in particular the manipulation of excitons as bosons, were stressed. This technique allows a closed solution without the use of a perturbation expansion and formally simplifies the consideration of interactions with photons or phonons. Previous calculations implying major disagreement between second quantized results and those obtained by first-order perturbation theory are incorrect. A detailed comparison of the two theories for a perfect one- dimensional aggregate shows in general good agreement. Thus the use of either formalism is valid, the choice dictated by convenience of one or the other in the particular problem studied.