  The Non-Equilibrium Green Function (NEGF) method was established in the
1960's through the classic work of Schwinger, Kadanoff, Baym, Keldysh and
others using many-body perturbation theory (MBPT) and the diagrammatic theory
for non-equilibrium processes. Much of the literature is based on the original
MBPT-based approach and this makes it inaccessible to those unfamiliar with
advanced quantum statistical mechanics. We obtain the NEGF equations directly
from a one-electron Schr\"odinger equation using relatively elementary
arguments. These equations have been used to discuss many problems of great
interest such as quantized conductance, (integer) quantum Hall effect, Anderson
localization, resonant tunneling and spin transport without a systematic
treatment of many-body effects. But it goes beyond purely coherent transport
allowing us to include phase-breaking interactions (both momentum-relaxing and
momentum-conserving as well as spin-conserving and spin-relaxing) within a
self-consistent Born approximation. We believe that the scope and utility of
the NEGF equations transcend the MBPT-based approach originally used to derive
it. NEGF teaches us how to combine quantum dynamics with "contacts" much as
Boltzmann taught us how to combine classical dynamics with "contacts", using
the word contacts in a broad, figurative sense to denote all kinds of
entropy-driven processes. We believe that this approach to "contact-ing" the
Schr\"odinger equation should be of broad interest to anyone working on device
physics or non-equilibrium statistical mechanics in general.
