Reconstruction of the Schrödinger-equation potential from scattering data by the Krein method

Reconstruction of the Schrödinger-equation potential (for the case of s-scattering) from scattering data by the Krein method is discussed. Analytically, the problem reduces to the solution of a system of linear inhomogeneous algebraic equations for certain functions. The Bargmann potentials, determined earlier by other methods, are shown to result from the solution of the problem for various particular cases.