Whittaker-Hill equation and semifinite-gap Schroedinger operators

Abstract

A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.

Revised version

References in corpus (2)

• Painlevé V and time dependent Jacobi polynomials
• On the rational monodromy-free potentials with sextic growth

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