Quantum Limits of the Electrostatic Image Force Theory

Abstract

The quantum mechanical problem of the interaction of a charged macroscopic body with a metal surface is treated by means of the variation method. The resulting expression for the interaction energy is the same as that obtained by the classical image force method except for three correction terms. These corrections are caused by the change in kinetic energy associated with the concentration of the electrons on the surface of the metal, the reduction in the electron-electron interaction energy in the metal resulting from the anti-symmetrization of the wave function and the effect of the finite thickness of the surface charge. It is found that these terms are negligible except for distances between the charged body and metal surface such that surface structure effects are important.