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Section 8.8: Exploring Wave Packets with Classical Analogies
Please wait for the animation to completely load.
Shown is a free quantum-mechanical wave packet. The top panel shows the wave functions in color-as-phase representation and the bottom panel shows the wave function in real-and-imaginary component representation. In the animation, ħ = 2m = 1. Restart.
The second animation, classical packet, depicts several balls, initially localized, but each row with a different velocity.7 The gray bar signifies the spread in the packet in the x direction.
- Why does the classical packet spread over time?
- Now look at the quantum-mechanical packet again. Why does it spread? Make sure to use quantum-mechanical arguments. Hint: can you come up with an analogy with the classical case shown here?
- What is the position-momentum correlation of each packet at t = 0? What is the position-momentum correlation of each packet at t = 2?
7This 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.