We consider the direct and inverse scattering for the n-dimensional Schroedinger equation with a potential having no spherical symmetry. Sufficient conditions are given for the existence of a Wiener-Hopf factorization of the corresponding scattering operator. This factorization leads to the solution of a related Riemann-Hilbert problem which plays a key role in inverse scattering.
Multidimensional inverse quantum scattering problem and Wiener-Hopf factorization
VAN DER MEE, CORNELIS VICTOR MARIA
1990-01-01
Abstract
We consider the direct and inverse scattering for the n-dimensional Schroedinger equation with a potential having no spherical symmetry. Sufficient conditions are given for the existence of a Wiener-Hopf factorization of the corresponding scattering operator. This factorization leads to the solution of a related Riemann-Hilbert problem which plays a key role in inverse scattering.
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