Polaron as the extended particle model

The polaron (a moving electron with concomitant lattice distortion) mass and energy are calculated. The problem of finding the Green function in the polaron model is solved. A number of the simplest approximations corresponding to the approximation in the picture of straight-line paths is considered. The case of strong coupling requires more detailed study of the particle motion in the effective field, caused by the significant polarization of vacuum near the particle. As a consequence, a more complex approximation of functional integrals is required. A variation method is used in this case. The bound state of a polaron interacting not only with photons, but also with some external classical field is investigated as well. A classical potential is considered as an example