Wave packet at a potential well - 1
Here we see a solution of the time-dependent Schrödinger equation with a rectangular potential well with radius R = 1.37 and depth V = -2. The incoming wave packet is a Gaussian with average momentum p =2 (in dimensionless units). The wave packet is sharply localized in momentum space and hence, inevitably, it is widely spread in position space.
The energy of the incoming wave packet is sharply localized in energy space near a maximum of the reflection coefficient. Hence a fairly large amount of the wave packet gets reflected.