The Rayleigh-Schr?dinger perturbation series of quasi-degenerate systems

摘要

We describe the first representation of the general term of the Rayleigh-Schr?dinger series for quasidegenerate systems. Each term of the series is represented by a tree and there is a straightforward relation between the tree and the analytical expression of the corresponding term. The combinatorial and graphical techniques used in the proof of the series expansion allow us to derive various resummation formulas of the series. A relation with several combinatorial objects used for special cases (degenerate or non-degenerate systems) is established.