S-Matrix for the One-Dimensional Schrödinger Equation and its Behaviour in the Quasi-Classical Region



A regular method is proposed for the direct calculation of the S-matrix for the one-dimensional Schrödinger equation. The method stays effective in case of the wide interaction regions ≫ λ and is applied to the investigation of the quasi-classical asymptote of the overbarrier reflection from arbitrary potentials. This asymptote is shown to be largely dependent on the continuity of the high derivatives of the potential.