95-249 Enss V., Weder R.

The Geometrical Approach to Multidimensional Inverse Scattering (70K, LaTeX 2.09) Jun 5, 95

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Abstract. 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 one of the Dollard scattering operators determines uniquely the total potential. We obtain as well a reconstruction formula with error term. Our simple proof uses a geometrical time--dependent method.

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