Scattering by singular potentials in coupled Schrödinger equations

Scattering in pairs of one-dimensional time-independent Schrödinger equations coupled via singular potentials are considered. For potentials given by Dirac’s delta function reflected and transmitted waves of the two modes as well as a bound state is found by integration. For potentials given by the derivative of Dirac’s delta function, resonant reflection and transmission occur for a discrete set of amplitudes of the scattering potential. These results depend on the applied regularization.