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The augmented-plane-wave (APW) method and the recently proposed pseudopotential method of Ziman are derived from the "scattered-wave" or Green's-function approach, thus establishing their connection with the original Korringa-Kohn-Rostoker (KKR) method. It is shown that the differences between these various band-theoretical techniques can be understood in terms of the particular choices for the representations and basis sets used in the expansions of the composite wave function and the Green's function. It is proven that the APW method leads to the most rapidly convergent representation in plane waves of the exact solution to the ordinary wave equation outside the "muffin-tin" spheres, while the KKR scheme yields the most rapidly convergent partial-wave or angular momentum representation of the exact solution to the Schr\"odinger problem within the spheres. The relative advantages of these methods in computing energy bands and one-electron wave functions are discussed.
K. H. Johnson (Fri,) studied this question.