In earlier work it was found that for prototype exciton-phonon systems (dimer, trimer) the spatial extension of the oscillatory wave functions strongly depends on the intrinsic material constants. In the present paper we demonstrate that this holds true also for extended systems with translational invariance. Our Hamiltonian is subjected to the Fulton-Gouterman (FG) transformation which exactly eliminates the excitonic degrees of freedom. The evolving FG equations elucidate most clearly the two counteracting tendencies of the model: self-trapping and anti-self-trapping. It is shown both analytically and variationally that, if these two tendencies are approximately equally strong, the phonon wave functions are spatially narrowed or broadened depending on the energetic region. This behavior can be adequately described by unitary squeezing transformations. © 1996 The American Physical Society.

• Received 28 July 1995

DOI:https://doi.org/10.1103/PhysRevB.53.3190