Exciton dispersion in a structure of N coupled multiple quantum wells

We derive analytic expressions for the exciton dispersion in N coupled quantum wells. The Förster-type interaction is taken as a mechanism of interwell coupling. The explicit N dependence is obtained, which shows that for any N the dispersion is continuous in all directions and the isolated quantum-well value is reached in the limit of ${\mathit{k}}_{\mathrm{\parallel }}$,${\mathit{q}}_{\nu }$→0 as is physically expected.