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Multi-dimensional inverse scattering theory for Schrödinger operators. (English) Zbl 0859.35083

The author considers the inverse scattering problem associated with the Schrödinger operator \(-\Delta+V\) in \(\mathbb{R}^3\), where the potential \(V\) is slowly decreasing at infinity. The investigation follows the Faddeev-Newton theory. The main results are: Characterization of the Green’s function of Faddeev and the scattering amplitude; reconstruction of the potential from the scattering amplitude of finite energies.

MSC:

35P25 Scattering theory for PDEs
81U40 Inverse scattering problems in quantum theory
35J10 Schrödinger operator, Schrödinger equation
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