Inverse scattering on the half-line revisited

The inverse scattering problem on the half-line has been studied in the literature in detail. V. Marchenko presented the solution to this problem. In this paper, the invertibility of the steps of the inversion procedure is discussed and a new set of necessary and sufficient conditions on the scattering data is given for the scattering data to be generated by a potential suitable potential. Our proof is new and in contrast with known proof it does not use equations on the negative half-line.