  We review the new theory of impure superconductors constructed by Kim and
Overhauser, and further developed by Kim. It was shown that Gor'kov's
self-consistency equation needs a pairing constraint derived from the Anomalous
Green's function. Whereas earlier studies have applied a constraint only on the
pair potential, we show that the kernel also should be fixed by the ground
state. The Bogoliubov-de Gennes equations need a pairing constraint in order to
obtain the proper vacuum state by the corresponding unitary transformation. The
relation between the pair potential and the gap parameter is clarified. This
new study opens up a reinvestigation of inhomogeneous superconductors. We will
discuss (i) strong coupling theory of dirty superconductors, (ii) suppression
of magnetic impurity effect by ordinary impurities, (iii) weak localization
correction to the phonon-mediated interaction, and (iv) other inhomogeneous
superconductors.
