  The non-equilibrium Green's function formalism for infinitely extended
reservoirs coupled to a finite system can be derived by solving the equations
of motion for a tight-binding Hamiltonian. While this approach gives the
correct density for the continuum states, we find that it does not lead, in the
absence of any additional mechanisms for equilibration, to a unique expression
for the density matrix of any bound states which may be present. Introducing
some auxiliary reservoirs which are very weakly coupled to the system leads to
a density matrix which is unique in the equilibrium situation, but which
depends on the details of the auxiliary reservoirs in the non-equilibrium case.
