Journal ArticleDOI
The sign-change argument revisited
TLDR
In this article, it is shown that the arguments leading to such a conclusion are not entirely justified and that the inapplicability of the sign-change argument in perturbation theory is critically analysed.About:
This article is published in Chemical Physics Letters.The article was published on 1980-11-15. It has received 4 citations till now. The article focuses on the topics: Sign (mathematics) & Argument.read more
Citations
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Journal ArticleDOI
The Devil's Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series
TL;DR: In this article, the authors use a plethora of examples to illustrate the cause of the divergence, and explain how this knowledge can be exploited to generate a hyperasymptotic approximation.
Journal ArticleDOI
Notes on polynomial perturbation problems
TL;DR: In this paper, the convergence behavior of Rayleigh-Schrodinger perturbation theory for polynomial perturbations is discussed with some specific examples and the choice of the perturbance parameter becomes crucial in this issue, in the light of certain seemingly contradictory conclusions drawn recently.
Journal ArticleDOI
Reply to “Another attack on the sign-change argument”
TL;DR: In this article, the applicability of the sign-change argument is clarified from a variational point of view, and the modus operandi of the said argument is explained.
Book ChapterDOI
Divergence of the Perturbation Series
TL;DR: The usefulness of the power series is conditioned by a fundamental question: its convergence as discussed by the authors, which is a fundamental problem in the RSPT (Chapter III) and the convergence of power series.
References
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Journal ArticleDOI
Divergence of perturbation theory in quantum electrodynamics
TL;DR: In this paper, an argument is presented which leads tentatively to the conclusion that all the power-series expansions currently in use in quantum electrodynamics are divergent after the renormalization of mass and charge.
Book ChapterDOI
Recent Developments in Perturbation Theory
TL;DR: Perturbation theory is designed to deal systematically with the effects of small perturbations on physical systems when the effects are mathematically too difficult to calculate exactly, and the properties of the unperturbed system are known as mentioned in this paper.
Journal ArticleDOI
Quantum Theory of Anharmonic Oscillators: Energy Levels of a Single and a Pair of Coupled Oscillators with Quartic Coupling
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Quantum-mechanical perturbation theory
TL;DR: In this paper, the convergence properties of perturbation series and Pade approximants are reviewed in the context of traditional results from the theory of real and complex variables, and the two major versions of time-independent perturbations theory, the Rayleigh-Schrodinger (RS) and Brillouin-Wigner (BW) theories, are compared and contrasted, and alternative techniques for evaluating the terms in the energy series are discussed.
Journal ArticleDOI
Asymptotic Properties of Perturbation Theory
TL;DR: In this paper, the perturbation expansions are derived by a technique which does not assume that convergent expansions exist, and criteria are developed to determine if a finite number of terms underestimates or overestimates the exact result for sufficiently small values of the coupling constant.