This applet implements a discrete lattice-gas formulation of the one-dimensional Schrodinger wave equation for a single particle. The wave function (usually represented by the Greek letter psi) is a complex-valued function of space and time, the magnitude-square of which is the probability of finding the particle at a given lattice site at a given time.
The intial conditions are a 37 node lattice with a sharply peaked wave function at the left. This wave function starts as a single wave fronts moving to the right. There is no potential field operating on the particle and the lattice has periodic boundaries.
The red plot is the magnitude-square of psi, the white plot is the real component of psi, and the yellow plot is the imaginary component. The simulation is not interactive, so sit back and watch it run.