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Inverse scattering problem for the 3-D Schrödinger equation and Wiener- Hopf factorization of the scattering operator. (English) Zbl 0724.47043

Summary: Sufficient conditions are given for the existence of a Wiener-Hopf factorization of the scattering operator for the 3-D Schrödinger equation with a potential having no spherical symmetry. A consequence of this factorization is the solution of a related Riemann-Hilbert problem, thus providing a solution of the 3-D inverse scattering problem.

MSC:

47N50 Applications of operator theory in the physical sciences
81U40 Inverse scattering problems in quantum theory
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
47A40 Scattering theory of linear operators
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