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**Multidimensional inverse scattering in an electric field.**
*(English)*
Zbl 0868.47011

In earlier articles Enss and Weder studied the inverse scattering in the following sense. Assume quantum mechanical systems with potentials only given as one member in a short range or long range function class, such that the scattering operator is known to exist. Then they can construct or discover the particular form of the potential for the system considered by properties of the scattering operator.

In the present article these methods are extended to quantum systems in presence of a constant electric field. In the two-body situation it is shown that the scattering operator determines uniquely the potential. The error term for this reconstruction is given in terms of the high velocity limit. In case of \(N\)-body particle systems with an electric field it turns out that the high velocity limit of any Dollard scattering operator determines the potential. The proofs are based on time-dependent methods used already in the articles by Enss and Weder mentioned above.

In the present article these methods are extended to quantum systems in presence of a constant electric field. In the two-body situation it is shown that the scattering operator determines uniquely the potential. The error term for this reconstruction is given in terms of the high velocity limit. In case of \(N\)-body particle systems with an electric field it turns out that the high velocity limit of any Dollard scattering operator determines the potential. The proofs are based on time-dependent methods used already in the articles by Enss and Weder mentioned above.

Reviewer: M.Demuth (Clausthal)

### MSC:

47A40 | Scattering theory of linear operators |

81U40 | Inverse scattering problems in quantum theory |