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A method is developed for obtaining directly from group-theoretical and topological considerations a consistent set of critical points belonging to a given secular equation. The treatment includes a detailed discussion of nonanalytic behavior near degeneracies. Comparison with many specific calculations shows that the minimal set so obtained is often the set actually present in the case of short-range forces. The contributions of nonanalytic critical points to the frequency distribution are analyzed. Behavior near critical points is made the basis of a scheme for calculating the main features of frequency distributions from the corresponding minimal sets. An approximate frequency distribution is calculated for aluminum. Possible applications to energy bands are discussed.
J. C. Phillips (Sat,) studied this question.