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

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