IMPROVED CALCULATION OF THE ELECTRON SELF-ENERGY DUE TO ELECTRON-PHONON COUPLING IN SOLIDS

An improved method for solving time-dependent problems in quantum mech anics, in the customary cases of constant or harmonic perturbation, is applied to the calculation of the self-energy of electrons interactin g with phonons in solids. The mixing of unperturbed Bloch states, resu lting from the actual coupling, is self-consistently taken into accoun t, and the related quantum probability amplitudes are determined throu gh direct integration over the quasiparticle spectrum. Laplace transfo rm and elementary mathematics are used, thereby enhancing the physical transparency, and bringing out approximations in every stage. Explici t illustrative results are worked out in the simple case of slowly var ying self-energy parameters. The method is critically compared with th e standard Green function approach, and further encourages more detail ed applications.