Please wait for the animation to completely load.
In Section 10.7 we saw that quantum wave packets in the infinite square well revive (reform at their original position and momentum with the exact same shape they had at t = 0). In Eq.(10.31) we stated the equation for the revival time, but what does this equation mean? In this Exploration we will give two two ways in which we can visualize this behavior.9
In the first set of animations, the ones with the racers, a number of objects (cars, runners, etc.)
race around a track. For simplicity, we allow the racers to pass each other by going through another racer. The angular
frequency of each racer is different in a special way: the angular frequency is an integer squared times the angular
speed of the slowest racer. In the second set of animations, the ones with the arrows, a number of arrows
in the complex plane (phasors) indicate the phase (from each e−iEnt/ħ
contribution) of a particular state in the infinite square well are shown. Their lengths are fixed and do not
represent amplitude. The angular frequency of each phasor is different in a special way: the angular frequency is an
integer squared times the angular speed of the slowest racer. Such a depiction is often called a
phase clock.
Answer the following questions for both the racer and phasor animations.
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9This Exploration is based in part on R. W. Robinett's talk, "Quantum Wave Packet Revivals" given at the 128th AAPT National Meeting, Miami Beach, FL, Jan. 24-28, 2004.