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Inverse scattering problem for two-dimensional Schrödinger operator. (English) Zbl 1111.35126
Summary: This work deals with the inverse scattering problem for two-dimensional Schrödinger operator. The following problem is studied: To estimate more accurately first nonlinear term from the Born series which corresponds to the scattering data with all energies and all angles in the scattering amplitude. This estimate allows us to conclude that the singularities and the jumps of the unknown potential can be obtained exactly by the Born approximation. Especially, for the potentials from $L^p$-spaces the approximation agrees with the true potential up to a continuous function.

35R30Inverse problems for PDE
81U40Inverse scattering problems (quantum theory)
35J10Schrödinger operator
35Q40PDEs in connection with quantum mechanics
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