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Inverse scattering in dimension two. (English) Zbl 0554.35126
The inverse scattering problem is solved for the two-dimensional time- independent Schrödinger equation. That is, the potential is reconstructed from the scattering amplitude, which is assumed to be known for all energies and angles. The reconstruction proceeds via a two- dimensional version of the Marchenko equation of one-dimensional inverse scattering. This work is based on Roger Newton’s method for the three-dimensional problem [J. Math. Phys. 21, 1698-1715 (1980; Zbl 0456.35070)].

MSC:
35R30 Inverse problems for PDEs
35J10 Schrödinger operator, Schrödinger equation
81U05 \(2\)-body potential quantum scattering theory
35P25 Scattering theory for PDEs
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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