Distribution of eigenvalues in gaps of the essential spectrum of Sturm-Liouville operators - a numerical approach

Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591, Eastham, Michael S. P., Hinz, Andreas M. and Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2004. Distribution of eigenvalues in gaps of the essential spectrum of Sturm-Liouville operators - a numerical approach. Journal Of Computational Analysis And Applications 6 (1) , pp. 85-95.

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Abstract

This paper reports on a new numerical procedure to count eigenvalues in spectral gaps for a class of perturbed periodic Sturm-Liouville operators. It is motivated by the desire to analyse the distribution of eigenvalues in the dense point spectrum of d-dimensional radially periodic Schrodinger operators. Our numerical results indicate that the well-known asymptotic formula for the largecoupling limit gives a good description already for moderate values of the coupling constant.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Last Modified:	20 Oct 2022 07:49
URI:	https://orca.cardiff.ac.uk/id/eprint/26498

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