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A generalized perturbation procedure is outlined which allows the interactions, induced by some potential, amongst a set of neighbouring energy levels to be treated exactly whilst the interactions between these levels and other more distant levels can be included as perturbations to any desired order. The procedure gives the usual results of both non-degenerate and degenerate perturbation theory as special cases.
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Fawcett et al. (1965) studied this question.
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