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Small-Energy Analysis for the Selfadjoint Matrix Schroedinger Operator on the Half Line

By Tuncay Aktosun, Martin Klaus and Ricardo Weder

Abstract

The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the most general selfadjoint boundary condition at the origin. When the matrix potential is integrable and has a first moment, it is shown that the corresponding scattering matrix is continuous at zero energy. An explicit formula is provided for the scattering matrix at zero energy. The small-energy asymptotics are established also for the corresponding Jost matrix, its inverse, and various other quantities relevant to the corresponding direct and inverse scattering problems.Comment: This published version has been edited to improve the presentation of the result

Topics: Mathematical Physics, Quantum Physics, 34L25, 34L40, 81U05, 81Uxx
Year: 2014
DOI identifier: 10.1063/1.3640029
OAI identifier: oai:arXiv.org:1105.1794
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