Small-energy asymptotics of the scattering matrix for the matrix Schrödinger equation on the line.(English)Zbl 1017.81046

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.

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
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References:

 [1] DOI: 10.1002/cpa.3160320202 · Zbl 0388.34005 [2] Alonso L. Mart{ı\'}nez, J. Math. Phys. 23 pp 2116– (1982) · Zbl 0505.35028 [3] DOI: 10.1143/PTP.52.397 · Zbl 1098.81714 [4] Olmedilla E., Inverse Probl. 1 pp 219– (1985) · Zbl 0614.35076 [5] Alpay D., Integral Equations and Operator Theory 30 pp 317– (1998) · Zbl 0896.34066 [6] Calogero F., Nuovo Cimento Soc. Ital. Fis., B 39 pp 1– (1977) [7] Klaus M., Inverse Probl. 4 pp 505– (1988) · Zbl 0669.34030 [8] Šeba P., J. Phys. A 19 pp 2573– (1986) · Zbl 0654.35076
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