Certain Explicit Relationships between Phase Shift and Scattering Potential

An intuitive account is given of recent important results of Gelfand and Levitan for the determination of the potential in the one-dimensional Schr\"odinger equation from the S-phase shift, the bound states, and certain normalizing parameters.The method is then used to obtain the first variation in the potential corresponding to a small change in the phase shift, bound states, and normalizing parameters.