For , free particles are scattered by a delta function potential. The positive-energy solutions can be written , with . The amplitudes of the transmitted and reflected waves are accordingly given by and , respectively. Note that these are the same for attractive and repulsive delta funtion potentials, independent of the sign of .

For continuum states, the graphic shows a wave incident from the left. The transmitted wave is shown on the right in blue and the reflected wave, on the left in red, with opacities indicating relative wave amplitudes.