  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.
