The technique consists of first dividing the conduction band into logarithmic intervals (i.e. intervals which get smaller exponentially as you move closer to the Fermi energy). One conduction band state from each interval is retained, this being the totally symmetric combination of all the states in that interval. The conduction band has now been "logarithmically discretized". The Hamiltonian is now in a position to be transformed into so-called linear chain form, in which the impurity is coupled to only one conduction band state, which is coupled to one other conduction band state and so on. Crucially, these couplings decrease exponentially along the chain, so that, even though the transformed Hamiltonian is for an infinite chain, one can consider a chain of finite length and still obtain useful results.