See https://dkirkby.github.io/quantum-demo/ for the jupyter notebook used to create this graphic and other similar material.

The real part of the component plane waves is shown in blue, with increasing wavenumber (decreasing wavelength) moving up the plot. Each component is vertically offset, for visual clarity, with a decreasing amplitude in order to localize the wave packet.

The sum of each plane is shown in red and represents the real part of the wave packet wave function.

Blue dots trace the motion of each plane from the initial wave packet center, each traveling at their phase velocity.

A red vertical line moves with the central group velocity.

The main points to note are:

• In the initial frame, the blue plane waves all interfere constructively at the center of the wave packet, but become progressively more incoherent moving away from the peak.
• Each blue plane wave propagates at a different phase velocity, causing the blue tracer dots to separate horizontally over time.
• Changes in the constant potential V0 lead to different phase velocities but an identical combined red wave function and group velocity.
• The center of the wave packet travels at the central group velocity indicated by the vertical red line.
• The red wave packet spreads as it propagates due to the variation of phase velocity with wavenumber.

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