Tunneling from a Many-Particle Point of View

Abstract

The Hamiltonian for a system of interacting electrons in the presence of a barrier is transformed into one which can be separated into three parts. Two of the parts describe the electrons on the "right" and "left" sides of the barrier, while the third is a transition term which allows tunneling through the barrier. It is shown that it is not reasonable to make the "right"- and "left"-hand Hamiltonians commute, but the effect of this failure is easily accounted for in perturbation theory. In addition, corrections to the transition operator arising from interelectronic interaction are written down and discussed briefly. They may be both quantitatively and qualitatively important.