Rayleigh–Schrödinger series and Birkhoff decomposition View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-07

AUTHORS

Jean-Christophe Novelli, Thierry Paul, David Sauzin, Jean-Yves Thibon

ABSTRACT

We derive new expressions for the Rayleigh–Schrödinger 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–Schrödinger series. Our results provide new combinatorial formulae and a new way 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. More... »

PAGES

1583-1600

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11005-017-1040-1

DOI

http://dx.doi.org/10.1007/s11005-017-1040-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1100679336


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