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Asymptotics of the scattering coefficients for a generalized Schrödinger equation
Journal of Mathematical Physics
The generalized Schrödinger equation d 2 /dx 2 ϩF(k)ϭ͓ikP(x)ϩQ(x)͔ is considered, where P and Q are integrable potentials with finite first moments and F satisfies certain conditions. The behavior of the scattering coefficients near zeros of F is analyzed. It is shown that in the so-called exceptional case, the values of the scattering coefficients at a zero of F may be affected 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.doi:10.1063/1.532920 fatcat:p6kgnift2nfo7ecrb6g2zu5mla