Darboux transformation for the Schrodinger equation with steplike potentials

The one-dimensional Schrodinger equation is considered when the potential is asymptotic to a positive constant on the right half line. The corresponding Darboux transformation is established by showing how the scattering solutions, the scattering coefficients, and the potential change when bound states are added or removed. The scattering coefficients are represented as certain integrals, from which their properties can be directly extracted. (C) 2000 American Institute of Physics. [S0022-2488(00)02304-5].