Simulation of potential barriers

Project members: 2

Simulation of an electrons behaviour when facing different kinds of potential barriers using Python and Matlab.

  1. We started by studying the behaviour of a gaussian wave packet that hits an infinite potential barrier, the interference pattern can be shown in the first image.
  2. Secondly we modelled a finite potential barrier and this time we could see the probability of tunnelling as a smaller (with less amplitude) wave packet that continues on at the right side of the barrier.
  3. Continuing on, we studied the behaviour of the wave package when hitting a potential step, with and without the occurrence of an electrical field (in the x-direction). This is known as Fowler-Nordheim tunnelling.
  4. Lastly we studied a case when we modelled the potential V(x)=-2/cosh^2(x) and sees a case when the wave packet starts to oscillate and passes the barrier, no reflection, the whole wave is transmitted. The potential is of the type Pöschl-Teller and for these kind of potentials, the Schrodinger Equation can be solved exactly and has the property of transmitting 100% of incoming waves.

Extract of Matlab code: