Adiabatic Theory of the Electron-Phonon Interaction

Abstract
Second-order corrections to the electronic energy due to the electron-phonon interaction have been obtained by several authors using the formalism of the adiabatic theory. Their result differs from the commonly accepted expression first given by Fröhlich in 1950. It will be demonstrated in the present paper that terms were omitted in the adiabatic theories which reconcile the two results. In addition, a comparison will be made between this paper and a recent paper along similar lines by Englman.