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On Perturbation Theory for the Sturm-Lio...

Kalitvianski, Vladim...

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On Perturbation Theory for the Sturm-Liouville Problem with Variable Coefficients by Kalitvianski, Vladimir ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	01-01-2009
Summary	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.
ISBN	-
Item Type	Article
File Type	pdf
File Size	36.88 KB
Language	English
Subjects	-
Unlimited	MYR 0.00
Total read	-
URL	http://arxiv.org/abs/0906.3504

Citation

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AMA 11th EditionReferences

Kalitvianski, Vladimir. On Perturbation Theory for the Sturm-Liouville Problem with Variable Coefficients. Australian National University. January 01, 2009. Accessed December 21, 2024. https://online.provdatabase.com/cite/2362

APA 7th EditionReferences

Kalitvianski, Vladimir. (2009). On Perturbation Theory for the Sturm-Liouville Problem with Variable Coefficients. Australian National University. https://online.provdatabase.com/cite/2362

Chicago 17th EditionReferences

Kalitvianski, Vladimir. On Perturbation Theory for the Sturm-Liouville Problem with Variable Coefficients. Australian National University. 2009. https://online.provdatabase.com/cite/2362

HarvardReferences

Kalitvianski, Vladimir. (2009). On Perturbation Theory for the Sturm-Liouville Problem with Variable Coefficients. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/2362. (Accessed 21 December 2024).

Harvard AustraliaReferences

Kalitvianski, Vladimir, 2009, On Perturbation Theory for the Sturm-Liouville Problem with Variable Coefficients, Australian National University, viewed 21 December 2024, <https://online.provdatabase.com/cite/2362>

MLA 9th EditionWorks Cited

Kalitvianski, Vladimir. On Perturbation Theory for the Sturm-Liouville Problem with Variable Coefficients. Australian National University, 2009. PROV Database, https://online.provdatabase.com/cite/2362.

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