Abstract

A computationally assisted proof of the existence of eigenvalues below the essential spectrum A. Zettl It is well known that the one-dimensional Schroedinger equation with potential $q(x)=\sin(x)$ on the half-line has an essential spectrum consisting of bands of continuous spectrum with no eigenvalues below its lowest point. Numerical experiments with SLEIGN2 indicate that the perturbed potential $q(x)=\sin(x + 1\( 1+ x^2))$ induces at least one eigenvalue below the essential spectrum. In this talk we show how methods of functional analysis and interval analysis may be used to prove this result. This is joint work with B. M. Brown and D. K. R. McCormack.

General Enquiries Dr. Malcolm Brown. Computer Science Cardiff University PO Box 916 Cardiff CF24 3XF, U.K. Malcom@cs.cf.ac.uk

N.B. All Mathematics appears in TeX/LaTeX source.

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