A quick psuedo-spectral solver for the time-dependent Schrödinger equation to convince myself I understood the method.
The Schrödinger equation describes the evolution of a quantum-mechanical wavefunction, and the norm of the wavefunction represents a probability density. The movie exhibits the phenomenon of quantum tunneling: when the particle reaches the potential barrier, it has a non-zero chance of appearing on the other side, despite having insufficient energy to do so classically.