Treatment of the Metallic Impurity Problem Using Green's Functions

The calculation of the charge density or spin density at an impurity in a metal is conveniently performed using a suitably weighted density of electron states. Working in the Wannier function representation, we derive this function making use of two Green's functions, one defined for the pure metal and the other for the metal containing the impurity. The former is directly related to the usual density of states of the pure metal, the latter to …