Equations of quantum inverse scattering problem in quasiclassical limit

Transition to the quasiclassical limit is studied in the framework of the Marchenko method for the inverse scattering problem at fixed angular momentum in the S-wave case. It is shown that the kernel of the transformation operator K(r, r') is determined by the classically forbidden region and is of exponential order. Thus the linear in-- tegral equation for K(r, r') cannot produce any relationships between quasiclassical physical quantities. Instead of this equation, the equivalent nonlinear equation for the gernel of the invesrse scattering transformation operator L(r, r') continued to the whole of the r eal axis with respect to the first argument. Under quasiclassical conditions, the kernel L(r, r') is a quickly oscillating function with a simple physical interpretation and the nonlinear equation for L(r, r') turns into the well-known quasiclassical relationship between the potential and the scattering phase. As an example, the S-wave scattering by an exponential potential is considered