In order to incorporate spatial inhomogeneity due to nonmagnetic impurities, Anderson [1] proposed a BCS-type theory in which single-particle states in such an inhomogeneous system are used. We examine Andersons proposal, in comparison with the Bogoliubov-de Gennes equations, for the attractive Hubbard model on a system with surfaces and impurities. [1] P. W. Anderson, J. Phys. Chem. Solids {bf 11}, 26 (1959).
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