01-250 Thomas Kriecherbauer, Christian Remling

Finite gap potentials and WKB asymptotics for one-dimensional Schr\"odinger operators (87K, LaTeX) Jul 9, 01

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Abstract. We study one-dimensional Schr\"odinger operators with power-decaying potentials. We prove that a previously obtained dimensional bound on exceptional sets of the WKB method is sharp in its whole range of validity. The construction relies on pointwise bounds on finite gap potentials. These bounds are proved by an analysis of the Jacobi inversion problem on hyperelliptic Riemann surfaces.

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