Steps and barriers

This simulation shows the propagation of a gaussian wavepacket when it hits a step or a barrier of potential. In this case there is no closed-form solution of the Schrödinger equation which is here solved numerically. The parameters are those of an electron moving in a semiconductor (GaAs). The initial kinetic energy is 200 meV and the potential height and shape can be changed. Time is slowed down by 14 orders of magnitude. When the step height is larger than the particle energy, a total reflexion can be observed, as in classical mechanics. Additionally, interferences are observed between the incident and reflected wave, when they overlap.
When the step height is larger than the particle energy, the particle is partially transmitted. This means that if we were to perform a measurement of the particle position, some measurements would find the particle has been transmitted and the others would find it has been reflected. The probabilities of these two events can be obtained by integrating the area of the transmitted or reflected wavepacket. Note that when the particle is transmitted, its speed is strongly reduced due to the decrease in kinetic energy, just like in classical mechanics.
Finally, when the potential is a barrier of finite thickness, there is a non-zero probability that the particle is transmitted through the barrier. This is the Tunnel effect.