Lavine, Richard B.; Nachman, Adrian I. On the inverse scattering transform for the \(n\)-dimensional Schrödinger operator. (English) Zbl 0736.35090 Topics in soliton theory and exactly solvable nonlinear equations, Proc. Conf. Nonlinear Evol. Equations, Solitons, Inverse Scattering Transform, Oberwolfach/Ger. 1986, 33-44 (1987). Summary: [For the entire collection see Zbl 0721.00016.]An open problem at the heart of multidimensional potential inverse scattering has been to determine whether the Faddeev-Lipman-Schwinger equation admits homogeneous solutions for real values of the appropriate parameters. We show that any reasonable potential with at least one bound state will give rise to such real exceptional points. We also include a brief review of the \(\bar\partial\) method which leads to this integral equation. Cited in 2 Documents MSC: 35Q40 PDEs in connection with quantum mechanics 35P25 Scattering theory for PDEs 35R30 Inverse problems for PDEs Keywords:time-independent Schrödinger equation; multidimensional potential inverse scattering; Faddeev-Lipman-Schwinger equation Citations:Zbl 0721.00016 PDFBibTeX XMLCite \textit{R. B. Lavine} and \textit{A. I. Nachman}, in: Symmetries and bi-Hamiltonian structures of 2+1 dimensional systems. . 33--44 (1987; Zbl 0736.35090)