Isozaki, Hiroshi Multi-dimensional inverse scattering theory for Schrödinger operators. (English) Zbl 0859.35083 Rev. Math. Phys. 8, No. 4, 591-622 (1996). 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. Reviewer: G.E.Karadzhov (Sofia) Cited in 7 Documents MSC: 35P25 Scattering theory for PDEs 81U40 Inverse scattering problems in quantum theory 35J10 Schrödinger operator, Schrödinger equation Keywords:Faddeev-Newton theory; Green’s function; scattering amplitude PDFBibTeX XMLCite \textit{H. Isozaki}, Rev. Math. Phys. 8, No. 4, 591--622 (1996; Zbl 0859.35083) Full Text: DOI