A direct method for constructing the canonical density matrix C(r, ro; beta ) for a single site problem using the complete set of normalized scattering solutions of the Schrodinger equation is described. For a spherical potential well the partial wave density matrices, Ci(r, r0, beta ), bring out several qualitative features. By this construction, it is shown that the information put into the many site problem of a liquid are on the same footing as in other single site approximations, namely, (i) phase shifts, and (ii) the radial distribution function. Since the Laplace transform of C(r, r0; beta ) is related to the Green function G(r, r0 -E), the usual Green functions of the conventional scattering theory can be used to compute C for simple systems. Finally, it is shown that the method of Rousseau, Stoddart and March (1970) for calculating the density of electronic levels in liquid metals is a single site approximation and is similar to the quasicrystalline approximation given by Ziman (1966).