Variational band theory of vibronic polarons in crystals. I. Preamble

We review the basic theoretical background for working out a variational band solution for vibronic polarons in crystals. It is based on the Lee-Low-Pines proposal as extended by Thomas et al. for describing Jahn-Teller polarons along a linear chain of atoms. The variational properties of antiadiabatic itinerant polarons are also discussed.