What is it?

It is a numerical method to solve for the time evolution of a State using Schrödinger's equation. It takes advantage of the Fast Fourier Transform, as the Hamiltonian terms depending on the momentum are simply computed in the Fourier Space. I animated the wavefunctions because I was always particularly curious about their 'physicality', and it is just beautiful to see how they are meant to develop with our own eyes. Note that the probability amplitude is plotted, rather than the wavefunction itself (which is complex valued.)