Page 10 - Physlets and Open Source Physics for Quantum Mechanics:

color represent the phase velocity of the wave packet. This phase velocity is exactly
half that of the group velocity, which is a well-known quantum-mechanical result.

Figure 11: The position and momentum space time evolution of the same quantum
wave packet in shown in Figure 9 now using the program QMSuperpositionFFTApp.
The wave packet is shown at t = 0, T rev/4, T rev/3, T rev/2, and T rev (T rev is set to 1).
During the revival time scale, the wave packet is usually spread out over the entire
length of the well. The exceptions occur at fractions of the revival time: pT rev/q,
where p and q are integers. In the top panels the wave function is shown in phase as
color representation and in the bottom panels the wave function is shown in
momentum space. The momentum-space wave function is useful in discerning the
multiple ‘mini-packets’ that arise during the fractional revivals.

On the revival time scale, as shown in Figure 11, the wave packet can reform into
localized wave packets. At T rev /4, two ‘mini-packets’ form at the exact same position,
but with opposite momentum. This is clearly depicted with the momentum-space wave
function, using the QMSuperpositionFFTApp program, in which two distinct momentum
distributions are present. At T rev /3, three mini-packets form. At half the revival time, t
= T rev /2, the wave packet also reforms, but at a location ‘mirrored’ about the center of
the well. One can see from the momentum-space wave function that the packet is
moving with ‘mirror’ (opposite) momentum values as well. Finally, at T rev, the wave
packet is exactly the same as when we started at
t = 0.