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A new approach is proposed to the solution of the quantum mechanical inversescattering problem at fixed energy. The method relates the fixed energy phaseshifts to those arising in an auxiliary Sturm-Liouville problem via theinterpolation theory of the Weyl-Titchmarsh m-function. Then a Marchenkoequation is solved to obtain the potential.

The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator