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arXiv · 1608.01110

Rayleigh-Schrödinger series and Birkhoff decomposition

Jean-Christophe Novelli·Thierry Paul·David Sauzin·Jean-Yves Thibon
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Abstract

We derive new expressions for the Rayleigh-Schrödinger seriesdescribing the perturbation of eigenvalues of quantumHamiltonians. The method, somehow close to the so-called dimensionalrenormalization in quantum field theory, involves the Birkhoffdecomposition of some Laurent series built up out of explicit fullynon-resonant terms present in the usual expression of theRayleigh-Schrödinger 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.

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Jean-Christophe Novelli, Thierry Paul, David Sauzin, Jean-Yves Thibon. 2017-01-19. Rayleigh-Schrödinger series and Birkhoff decomposition. https://doi.org/10.1007/s11005-017-1040-1

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