Tight-binding optical polaron in the adiabatic limit

The problem of a tight-binding polaron interacting with the longitudinal optical phonons in a polar crystal is investigated in the adiabatic limit. A Pekar-type variational wavefunction, including a tight-binding electronic part is used in order to get the ground-state energy of the system. We find and characterize two limiting cases: a self-trapped state for large coupling and a band state for smaller electron-phonon interactions. The continuum Fröhlich limit can also be found from our approach.