The second-order energy in Rayleigh-Schrödinger single perturbation theory for a degenerate level with two perturbations is written in "double perturbation" form. The difficulties in formal double perturbation theory are avoided.
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We are grateful to Professor S.T. Epstein for helpful discussions on this problem. One of us (K.B.L.) would like to acknowledge the support of the Science Research Council (U.K.). We would also like to acknowledge the support of the U.S. Army through its European Research Office.