Quantum simulation of a particle breaking through a Sierpinski carpet fractal potential

This video shows the particles hitting Sierpinski carpets at different iteration orders. All particles have the same mean initial momentum and therefore the same wavelength. As shown in the video, gets trapped relatively easily in low Sierpinski iteration order. This happens because it is exciting the resonant eigenstates of the structure. When the Sierpinski order is enough to make the separation of the blocks smaller than the wavelength, the particle is unable to penetrate it. When this is the case It can be shown analytically that the wavefunction amplitude decays exponentially inside the carpet. In this case, no resonant eigenstates are excited. The Schrödinger equation was solved using a Split Fourier method, which is a method to solve the time-dependent Schrödinger equation. It involves splitting the computations of each time step in the momentum space and position. The simulator used is QMsolve, an open-source python open-source package for visualizing and solving