Green function solution of a second-order partial differential equation and conductivity of thin films

Correct form of the Green function G of the Schrödinger equation is developed for a thin metallic film of thickness d which contains infinitesimally weak volume and surface scatterers. Conductivity σ of the film is obtained from the imaginary part of the self-energy Σ appearing in the average G and increases smoothly with d and that density of states is not staircaselike as contrast to the usual. Examination of σ in terms of d agrees well with the experiment.