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On the large order expansion for the anharmonic oscillators

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Abstract

Using functional approaches, we investigate the large-K behaviour of theK th coefficientE k in the perturbation expansion for the ground-state energyE(g) of the generalized anharmonic oscillatorX 2N with internalO(n)-symmetry. We establish the equivalence between the pure functional approach and the method of Collins-Soper at any order in 1 /K. For that purpose, we first develop an algebraic treatment of perturbation series and prove a theorem on Borelsummable functions. Finally, we compute analytically the 1 /K and 1 /K 2 corrections to the leading term forN=2.

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  1. V. R. Figerou

    Present address: Department of Physics, The Rockefeller University, 10021, New York, NY, USA

Authors and Affiliations

  1. Département de Physique Mathématique, U.S.T.L., F-34060, Montpellier Cedex, France

    V. R. Figerou

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  1. V. R. Figerou
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Communicated by J. Ginibre

Physique Mathématique et Théorique, Equipe de Recherche associée au C.N.R.S.

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Figerou, V.R. On the large order expansion for the anharmonic oscillators. Commun.Math. Phys. 79, 401–433 (1981). https://doi.org/10.1007/BF01208501

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  • DOI: https://doi.org/10.1007/BF01208501

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