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 an error term. Our simple proof uses a geometrical time-dependent method.

Abstract.A new (geometrical) proof is given for the asymptotic completeness of the wave operators and the absence of a singular continuous spectrum of the Hamiltonian for potentials which decrease faster than in the Coulomb case, the space dimension is arbitrary.

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