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arXiv · 1206.2986

High-Energy analysis and Levinson's theorem for the selfadjoint matrix Schroedinger operator on the half line

Tuncay Aktosun·Ricardo Weder
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Abstract

The matrix Schroedinger equation with a selfadjoint matrix potential is considered on the half line with the general selfadjoint boundary condition at the origin. When the matrix potential is integrable, the high-energy asymptotics are established for the related Jost matrix, the inverse of the Jost matrix, and the scattering matrix. Under the additional assumption that the matrix potential has a first moment, Levinson's theorem is derived, relating the number of bound states to the change in the argument of the determinant of the scattering matrix.

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Tuncay Aktosun, Ricardo Weder. 2012-06-14. High-Energy analysis and Levinson's theorem for the selfadjoint matrix Schroedinger operator on the half line. https://doi.org/10.1063/1.4773904

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