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

Aktosun, Tuncay; Klaus, Martin; van der Mee, Cornelis

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.

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

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