Enss V., Weder R.
The Geometrical Approach to Multidimensional Inverse Scattering
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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.