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Dept. of Mathematics and Computer Science (Berlin)

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reviewer: Miloslav Znojil

reviewernum: 9689

revieweremail: znojil@ujf.cas.cz

zblno: DE014343024

author: L. Skala, J. Cizek and J. Zamastil

shorttitle: Strong coupling perturbation expansions for anharmonic oscillators

source: J. Phys. A: Math. Gen. 32, No 30, 5715 - 5734 (1999)

rpclass: 81Q15

rsclass: 47A55; 47N50; 65B10; 34L15; 34L40; 81T15

keywords: Rayleigh Schroedinger perturbation series, anharmonic oscillators

revtext: A typical user of quantum mechanics is given a phenomenological Hamiltonian (say, quartic, sextic, octic or decadic anharmonic oscillator) and constructs a low lying part of its spectrum via the usual (and comparatively easily generated, so called Rayleigh-Schroedinger) perturbation series. Such a user is given a significant help by the present paper. Firstly, he/she is advised to get rid of the divergence by moving to the strong-coupling (SC) and renormalized strong-coupling (RSC) regime via a suitable re-definition of the coupling strength. This advice is accompanied by a number of formulae, Tables and Figures which demonstrate the survival of an easy feasibility of the recipe and illustrate the numerous specific merits of the RSC approach. One is particularly impressed by the observation that the RSC perturbation series behaves as convergent for all the real values of the renormalized coupling (i.e., in particular, far beyond the single well regime: the next paper [20] by the same authors will say more) and that it is able to provide the upper and upper energy bounds in a way simplifying the current SC predictions significantly.

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