Partitioning Method and Van Vleck's Perturbation Theory

Energy expressions to fourth order are -given for a degenerate zeroth order state by the use of a partitioning process in relation to Van Vleck's transformation. Double perturbation is discussed as a natural extention of this treatment. The mathematical essence of Dalgarno's interchange theorem is reinterpreted. By using this interpretation, it is demonstrated that there are more than one accessible correlation expressions of the interchange theorem for degenerate zeroth order states. It is also discussed whether or not the difficulty in obtaining the interchange theorem for a degenerate case remains.