Schroedinger-Stermer equation in direct and inverse scattering problems

It is shown how to formulate boundary conditions for the Schroedinger-Stermer (SS) equation without using starting methods, what is of a principle significance for the solution of a relevant finite-difference (fd) inverse problem. The same rule is valid for other higher-order fd approximation for the Schroedinger equation and for finite element methods with nonlinear splines. A generalization for the R-matrix scattering theory for the SS equation is suggested. The recursion relations are derived, which provide for the solution of the inverse problem for the SS equation