This is an animated visualization of the behavior of a pure sinusoidal wavefunction in one dimension, representing a free quantum particle with a precise momentum that is inversely proportional to the wavelength. There is no potential energy and the particle is nonrelativistic, so the phase velocity is directly proportional to the momentum.
You can plot either the real and imaginary parts of the wavefunction (shown in orange and blue, respectively), or the probability density and phase, with the phase represented by hues going from red (pure real and positive) to light green (pure imaginary and positive) to cyan (pure real and negative) to purple (pure imaginary and negative) and finally back to red. For a pure sinusoidal wavefunction, the probability density is the same everywhere.
By Daniel V. Schroeder, Physics Dept., Weber State University