Rayleigh-Schrödinger series and Birkhoff decomposition
Résumé
We derive new expressions for the Rayleigh-Schr\"odinger series
describing the perturbation of eigenvalues of quantum
Hamiltonians. The method, somehow close to the so-called dimensional
renormalization in quantum field theory, involves the Birkhoff
decomposition of some Laurent series built up out of explicit fully
non-resonant terms present in the usual expression of the
Rayleigh-Schr\"odinger series.
Our results provide
new combinational formulae and a new way \ff{of deriving} perturbation series in Quantum Mechanics. More generally we prove that such a decomposition provides solutions
of general normal form problems in Lie algebras.
| Origine | Fichiers produits par l'(les) auteur(s) |
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