Polarons in the harmonic lattice. I. Standing polaron
  We obtain analytical expressions for the large- and small-radius polarons on the one-dimensional lattice in the TBA approximation. The equations of motion for this model are treated classically for the oscillator subsystem, while a quantum description is used for the electron. The electron-phonon interaction is considered in the linear Su--Schrieffer--Heeger approximation. Good agreement between analytical formulae and accurate numerical simulation is obtained. The dynamics of polaron formation from different initial conditions is considered. Some features of the wave function evolution, governed by the finite lattice length, are elucidated. 
V. N. Likhachev, T. Yu. Astakhova, G. A. Vinoghradov
cond-mat.mes-hall physics.bio-ph