Self-Similar Perturbation Theory

Details Self-Similar Perturbation Theory Self-Similar Perturbation Theory

1999-11-15

arxiv.org/abs/hep-ph/9911357v1

Annals Phys. 277 (1999) 219-254

Physics

High Energy Physics

High Energy Physics - Phenomenology

1 file, 45 pages, LaTex

Scientific paper

10.1006/aphy.1999.5953

A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather delicate questions: What can be said about the convergence of the calculational procedure when only a few its terms are available and how to decide which of the initial approximations of the perturbative algorithm is better, when several such initial approximations are possible? Definite answers to these important questions become possible by employing the self-similar perturbation theory. The novelty of this paper is in developing the stability analysis based on the method of multipliers and in illustrating the efficiency of this analysis by different quantum-mechanical problems.

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