Asymptotics of the Scattering Coefficients for a Generalized Schr Odinger Equation

The generalized Schrr odinger equation d 2 =dx 2 + F (k) = ikP (x) + Q(x)] is considered, where P and Q are integrable potentials with nite rst moments and F satisses certain conditions. The behavior of the scattering coeecients near zeros of F is analyzed. It is shown that in the so-called exceptional case, the values of the scattering coeecients at a zero of F may be aaected by P (x): The location of the k-values in the complex plane where the exceptional case can occur is studied. Some examples are provided to illustrate the theory.