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In his renormalization paper of the Kondo effect Wilson replaced the fullband of s-electrons by a small number of ''Wilson states''. He started from arather artificial symmetric band with constant density of states and constantinteraction with the impurity. It is shown in the present paper that with aminor modification the Wilson states are optimally suited to treat theinteraction of an impurity with an arbitrary s-band. Each Wilson staterepresents electrons of a whole energy range. It carries the interaction of allthese electrons with the impurity. All the other electron states in this energyrange have zero interaction with the impurity and are neglected in thecalculation. The resulting error is minor. As an example the singlet-tripletexcitation energy of a Kondo impurity is numerically calculated for atight-binding band with a strongly energy dependent density of states.

The Friedel-Anderson and Kondo Impurity Problem for Arbitrary s-Band Density of States and Exchange Interaction