Perturbation formalism nondegenerate

In this context equations (50) and (53) can be considered forming a completely general perturbation theory for nondegenerate systems, although a recent development permits to extend the formalism to degenerate states [lej. 

We shall restrict the discussion here to nondegenerate perturbation theory for the ground-state case. However, there is no formal difficulty extending the method to degenerate cases if we wish to treat excited states (Cizek and Vrscay, 1982 Adams et al, 1980). 

Quasi-degeneracy Effects.—The convergence properties of the non-degenerate formulation of the many-body perturbation theory deteriorate when quasidegeneracy is present in the reference spectrum. In view of its simplicity, however, there is considerable interest in exploring the range of applicability of the nondegenerate formalism. 

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