  In this paper we address the topic of inelastic electron scattering in
mesoscopic quantum transport. For systems where only elastic scattering is
present, Landauer theory provides an adequate description of transport that
relates the electronic current to single-particle transmission and reflection
probabilities. A formalism proposed recently by Bonca and Trugman facilitates
the calculation of the one-electron transmission and reflection probabilities
for inelastic processes in mesoscopic conductors connected to one-dimensional
ideal leads. Building on their work, we have developed a self-consistent
procedure for the evaluation of the non-equilibrium electron distributions in
ideal leads connecting such mesoscopic conductors to electron reservoirs at
finite temperatures and voltages. We evaluate the net electronic current
flowing through the mesoscopic device by utilizing these non-equilibrium
distributions. Our approach is a generalization of Landauer theory that takes
account of the Pauli exclusion principle for the various competing elastic and
inelastic processes while satisfying the requirement of particle conservation.
As an application we examine the influence of elastic and inelastic scattering
on conduction through a two site molecular wire with longitudinal phonons using
the Su-Schrieffer-Heeger model of electron-phonon coupling.
