Transmission, reflection, and resonance formation in one-dimensional systems

A method is developed that treats on equal footing bound states, resonance formation, and scattering problems in one-dimensional systems. The approach allows one to deal with nonlocal, energy-dependent potentials and is conceptually analogous to the variable phase method where the role of the scattering phase and the amplitude functions is played by nonlocal reflection and transmission functions. The formal results are illustrated and analyzed by simple examples and the physical significance of these examples is pointed out.