  The ground-state energy, the effective mass and the number of virtual phonons
of the optical large polaron confined strictly in one dimension have been
estimated by using the generalized Gaussian approximation. The leading-order
terms take care of all Gaussian fluctuations in the system and improve the
conventional variational estimates at finite coupling. Particularly, the lowest
upper bound to the polaron ground-state energy has been obtained. The
non-Gaussian contributions systematically correct the leading-order
approximations. We have obtained exact analytical solutions in the weak- and
strong-coupling limit and reasonable numerical data for intermediate coupling.
Our result for the number of excited phonons limits the validity region of the
few-phonon approximation methods.
