Wave scattering in 1-D nonconservative media

In this review paper, the generalized Schrodinger equation d(2) psi/dx(2) + k(2) psi = [ikP(x)+ Q(x)]psi is considered, where P(x) and Q(x) are real, integrable potentials with finite first moments. The scattering solutions and the bound state solutions are studied, the scattering coefficients and their small-k and large-k asymptotics are analyzed. Unless P(x) less than or equal to 0, it is shown that there may be bound states at complex energies, degenerate bound states, and singularities of the transmission coefficient for real k. Some illustrative examples are provided.