Electron-Phonon Interaction by the Method of Pseudo-potentials

The matrix element is calculated (1) for orthogonalized plane waves assuming that the ion moves rigidly and (ii) for the equivalent plane waves on the assumption that the net effective potential (Hartree-Fock potential plus pseudo-potential) moves rigidly with the ion. It is shown that these two results are equivalent if the pseudo-potential operator can be treated as a localized potential.