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Scattering for the Schrödinger Equation in Multidimensions. Nonlinear δ-Ewuation, Characterization of Scattering Data and Related Results-Chapter 6.2.4

Elsevier Ltd
DOI: 10.1016/b978-012613760-6/50097-8


Publisher Summary This chapter presents the direct and inverse scattering for the Schrödinger equation, and nonoverdetermined inverse scattering for the Schrödinger equation in multidimensions. The characterization problem, which consists of finding necessary and sufficient conditions for a function f on M in order to be the scattering amplitude for a potential v satisfying a given equation, is considered often as the most interesting problem of inverse scattering. More generally, any method of reconstructing a potential from its scattering amplitude and any method for calculating the scattering amplitude for a potential imply a method of verification whether a function is the scattering amplitude for a potential. Therefore, those characterizations of the scattering amplitude that provide methods of the verification in question simpler than the elementary approach are of particular interest.

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