The density of states and the spectral shift density of random Schrodingeroperators

In this article we continue our analysis of Schrodinger operators with a ra ndom potential using scattering theory. In particular the theory of Krein's spectral shift function leads to an alternative construction of the densit y of states in arbitrary dimensions. For arbitrary dimension we show existe nce of the spectral shift density, which is defined as the bulk limit of th e spectral shift function per unit interaction volume. This density equals the difference of the density of states for the free and the interaction th eory. This extends the results previously obtained by the authors in one di mension. Also we consider the case where the interaction is concentrated ne ar a hyperplane.