Calculation of the Scattering Potential from Reflection Coefficients

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Abstract
It is shown how the scattering potential can be calculated from suitably defined reflection coefficients in the case of the one- and three-dimensional reduced wave equations by means of a formal series expansion. The more general problem of calculating scattering potentials from elements of the scattering operator is also discussed and it is shown that to calculate the scattering potential it is often sufficient to prescribe the representation in which it is to be diagonal.

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