Scattering amplitudes and bound state energies for one-dimensional, weak potentials

It is emphasized that one-dimensional, weak potentials have some special properties. They sustain a bound state provided the potential is attractive, and the transmission coefficient for them vanishes in the low energy limit. It is pointed out that a perturbation series for the inverse of the scattering amplitude provides a convenient expression for the analysis of these properties. (C) 1999 American Association of Physics Teachers