Visual Quantum Mechanics

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Wave packet at a potential well - 2

Here we see a solution of the time-dependent Schrödinger equation with a rectangular potential well with radius R = 1.7 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.

Here the radius of the well is slightly larger than in the previous movie. Due to the dependence of the reflection coefficient on the radius of the potential well, the average energy of the incoming wave packet is now close to a minimum of the reflection coefficient. Now a much smaller amount of the wave packet gets reflected, although the well is thicker than in the previous movie.