Scattering at a wide potential well

A Gaussian wave packet is scattered at a wide rectangular well. You can see that reflections happen at every potential step. Hence the reflected wave packet consists of two well distinguished peaks (a Schrödinger-cat state).

From the Fourier transform of the wave packet in the lower image we can infer the momentum distribution. You can see that the right-moving part of the wave packet temporarily gets faster during the transition through the well (note also the shorter wave length in position space). At the same time a reflected (left-moving) part is formed. As soon as the right-moving wave packet hits the second step at the far end of the well, it gets slower again and a fast left-moving part emerges. When this part finally leaves the well at the left-hand side, the reflected wave packet becomes similar to the Schrödinger-cat state shown here. Note, in particlular, the characteristic pattern in the momentum distribution.