Exact free-particle solution of the Schrödinger equation. Upper dots are the real and imaginary parts of psi. The middle cloud is sampled from the probability density and follows the probability current. The lower cloud is the momentum distribution, which does not spread. Sound is ψ itself, read across the packet. Left is real, right is imaginary. Pitch follows momentum. The chirp is dispersion.
ψ(x)
|ψ|²
|φ(k)|²