On Perturbation Theory for the Sturm-Liouville Problem with Variable Coefficients
| Autor: | Kalitvianski, Vladimir |
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| Rok vydání: | 2009 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Original study, 29 pages, 20 figures, corrected and improved text and formulas |
| Databáze: | arXiv |
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