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The geometrical approach to multidimensional inverse scattering. (English) Zbl 0849.35094

Authors’ summary: We prove that in multidimensional short-range potential scattering the high velocity limit of the scattering operator of an \(N\)-body system determines uniquely the potential. For a given long-range potential the short-range potential of the \(N\)-body system is uniquely determined by the high velocity limit of the modified Dollard scattering operator. Moreover, we prove that any cone of the Dollard scattering operators determines uniquely the total potential. We obtain as well a reconstruction formula with an error term. Our simple proof uses a geometrical time dependent method.

MSC:

35P25 Scattering theory for PDEs
81U40 Inverse scattering problems in quantum theory
81U10 \(n\)-body potential quantum scattering theory
35R30 Inverse problems for PDEs
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