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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.

MSC:

35Q40 PDEs in connection with quantum mechanics
35P25 Scattering theory for PDEs
35R30 Inverse problems for PDEs

Citations:

Zbl 0721.00016
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