Aktosun, Tuncay; Klaus, Martin; van der Mee, Cornelis Small-energy asymptotics of the scattering matrix for the matrix Schrödinger equation on the line. (English) Zbl 1017.81046 J. Math. Phys. 42, No. 10, 4627-4652 (2001). Summary: The one-dimensional matrix Schrödinger equation is considered when the matrix potential is self-adjoint with entries that are integrable and have finite first moments. The small-energy asymptotics of the scattering coefficients are derived, and the continuity of the scattering coefficients at zero energy is established. When the entries of the potential have also finite second moments, some more detailed asymptotic expansions are presented. Cited in 15 Documents MSC: 81U20 \(S\)-matrix theory, etc. in quantum theory 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 34L25 Scattering theory, inverse scattering involving ordinary differential operators 34A55 Inverse problems involving ordinary differential equations Keywords:integrable matrix entries; finite first moments; small-energy asymptotics; scattering coefficients PDFBibTeX XMLCite \textit{T. Aktosun} et al., J. Math. Phys. 42, No. 10, 4627--4652 (2001; Zbl 1017.81046) Full Text: DOI Link References: [1] DOI: 10.1002/cpa.3160320202 · Zbl 0388.34005 · doi:10.1002/cpa.3160320202 [2] Alonso L. Mart{ı\'}nez, J. Math. Phys. 23 pp 2116– (1982) · Zbl 0505.35028 · doi:10.1063/1.525265 [3] DOI: 10.1143/PTP.52.397 · Zbl 1098.81714 · doi:10.1143/PTP.52.397 [4] Olmedilla E., Inverse Probl. 1 pp 219– (1985) · Zbl 0614.35076 · doi:10.1088/0266-5611/1/3/007 [5] Alpay D., Integral Equations and Operator Theory 30 pp 317– (1998) · Zbl 0896.34066 · doi:10.1007/BF01195586 [6] Calogero F., Nuovo Cimento Soc. Ital. Fis., B 39 pp 1– (1977) · doi:10.1007/BF02738174 [7] Klaus M., Inverse Probl. 4 pp 505– (1988) · Zbl 0669.34030 · doi:10.1088/0266-5611/4/2/013 [8] Šeba P., J. Phys. A 19 pp 2573– (1986) · Zbl 0654.35076 · doi:10.1088/0305-4470/19/13/022 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.