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.

 

Watch both the classical packet and quantum-mechanical packet animations.

  1. Why does the classical packet spread over time?

  2. 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?

  3. What is the position-momentum correlation of each packet at t = 0?  What is the position-momentum correlation of each packet at t = 2?

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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.

 

 

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