Anderson prescription for surfaces and impurities

We test the Anderson prescription, a BCS formalism for describing supercond uctivity in inhomogeneous systems, and compare results with those obtained from the Bogoliubov-de Gennes formalism, using the attractive Hubbard model with surfaces and nonmagnetic impurities. The Anderson approach captures t he essential features of the spatial variation of the gap parameter and ele ctron density around a surface or an impurity over a wide range of paramete rs. It breaks down, however, in the strong-coupling regime for a weak impur ity potential.