  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.
