Rayleigh-Schrödinger series and Birkhoff decomposition - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Letters in Mathematical Physics Année : 2018

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.
Fichier principal
Vignette du fichier
rayschrfinal.pdf (269.71 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01351108 , version 1 (02-08-2016)
hal-01351108 , version 2 (14-01-2017)

Identifiants

Citer

Jean-Christophe Novelli, Thierry Paul, David Sauzin, Jean-Yves Thibon. Rayleigh-Schrödinger series and Birkhoff decomposition. Letters in Mathematical Physics, 2018, 108 (7), pp.1583-1600. ⟨10.1007/s11005-017-1040-1⟩. ⟨hal-01351108v2⟩
739 Consultations
190 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More