Scattering theory in narrow energy bands - Application to Wolff-Kondo Hamiltonian equivalence

A theory of transition metal impurities in transition metal hosts is formulated. In this theory the concept of scattering states is transferred from potential scattering in free space to the realm of scattering in a host lattice. It is demonstrated that scattered waves can be defined which are almost eigenstates of the problem (in the sense that they are normalized and orthogonal in the continuum limit where the volume is large and the adiabatic switching parameter tends to zero). The scattering states are used to express the Wolff model in the form of an Anderson type model and from there it is shown that the Wolff model is equivalent to a Kondo model.