The Rayleigh-Schrödinger perturbation series of quasi-degenerate systems

Details The Rayleigh-Schrödinger perturbation series of quasi-degenerate systems The Rayleigh-Schrödinger perturbation series of quasi-degenerate systems

2010-11-08

arxiv.org/abs/1011.1751v1

Physics

Quantum Physics

16 pages, 3 figures

Scientific paper

We present the first representation of the general term of the Rayleigh-Schr\"odinger 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. The relation with several combinatorial objects used for special cases (degenerate or non-degenerate systems) is established.

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