  A resolvent formalism is applied to the problem of inelastic scattering of an
electron linearly coupled to a set of phonon modes. It is shown how the many
phonon mode coupling and excitation can be reduced to a single phonon mode
description, consistent with other approaches to the phenomenon of inelastic
tunneling in heterostructures. A unifying connection is made with the phenomena
of resonant electron scattering through molecules in the gas phase and of
tunneling of electrons through adsorbates in scanning tunneling microscopy.
