Perturbation theory for the Sturm-Liouville problem with variable coefficients
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Publication:1842355
zbMATH Open0818.34015arXiv0906.3504MaRDI QIDQ1842355
Author name not available (Why is that?)
Publication date: 15 May 1995
Published in: (Search for Journal in Brave)
Abstract: In this article I study different possibilities of analytically solving the Sturm-Liouville problem with variable coefficients of sufficiently arbitrary behavior with help of perturbation theory. I show how the problem can be reformulated in order to eliminate big (or divergent) corrections. I obtain correct formulas in case of smooth as well as in case of step-wise (piece-constant) coefficients. I build simple, but very accurate analytical formulae for calculating the lowest eigenvalue and the ground state eigenfunction. I advance also new boundary conditions for obtaining more precise initial approximations. I demonstrate how one can optimize the PT calculation with choosing better initial approximations and thus diminishing the perturbative corrections. Dressing, Rebuilding, and Renormalizations are discussed in Appendices 4 and 5.
Full work available at URL: https://arxiv.org/abs/0906.3504
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