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Title: Small-energy analysis for the selfadjoint matrix Schrödinger operator on the half line. II

The matrix Schrödinger 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 second moment, it is shown that the corresponding scattering matrix is differentiable at zero energy. An explicit formula is provided for the derivative of the scattering matrix at zero energy. The previously established results when the potential has only the first moment are improved when the second moment exists, by presenting the small-energy asymptotics for the related Jost matrix, its inverse, and various other quantities relevant to the corresponding direct and inverse scattering problems.
Authors:
 [1] ;  [2] ;  [3]
  1. Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019-0408 (United States)
  2. Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061 (United States)
  3. Departamento de Física Matemática, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Apartado Postal 20-126, Col. San Angel, C.P. 01000, México D.F., México (Mexico)
Publication Date:
OSTI Identifier:
22251154
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 3; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; BOUNDARY CONDITIONS; ENERGY ANALYSIS; EQUATIONS; INVERSE SCATTERING PROBLEM; MATRICES; POTENTIALS; SCATTERING