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Spectral Concentration for Perturbed Equations of Harmonic Oscillator Type

Published online by Cambridge University Press:  01 February 2010

B. M. Brown  and
M. S. P. Eastham
B. M. Brown
Affiliation:
Department of Computer Science, Cardiff University, PO Box 916, Cardiff CF24 3XF, malcolm@cs.cf.ac.uk
M. S. P. Eastham
Affiliation:
Department of Computer Science, Cardiff University, PO Box 916, Cardiff CF24 3XF

Abstract

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Sturm–Liouville potentials of the form xa ƒ(∈x) are considered, where a > 0, ƒ decays sufficiently rapidly at infinity, and ∈ is a small positive parameter. It is shown that there are a finite number N(∈) of spectral concentration points, and computational evidence is given to support the conjecture that N(∈) increases to infinity as ∈ decreases to zero.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 3 , 2000 , pp. 76 - 85
Copyright
Copyright © London Mathematical Society 2000

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