If you were to set this up as a Schrödingers classical wave equation with a periodic boundary condition, (real and imagined parts) in one dimension, it would ev

If you were to set this up as a Schrödingers classical wave equation with a periodic boundary condition, (real and imagined parts) in one dimension, it would evolve exactly in this way into its own Fourier transform and then back. (Referring to the image of the square wave evolving into a sinc function halfway down the page). I only know this because I simulated it, I don’t know why that is the case. Perhaps someone better at the math can fill in the details.