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- Copyright 2000 John S. Winn. All rights reserved. Last updated September 23, 2000.
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This page supplements Problem 11.21 on page 385.
Two eigenfunctions y1 and y2 are "mixed" to make a new wavefunction Y as described in the problem.
The top graph animates the energy expectation value, <E>, on the left, and the probability Y2 and the position expectation value, <x>, on the right. The right graph also shows the probabilities for both eigenfunctions as gray curves. The center graph maps the mixing angle g. Click on the graph to start or stop the animation. As the mixing angle changes, the energy bars for the two pure eigenfunctions change shade to animate the degree of mixing.
Allow the animation to run for several cycles as you study and compare the graphs. Note how the animated probability overlaps that for the pure states at mixing angles corresponding to "no mixing." Static graphs of <x> and <E> are shown at the bottom of the page below the equations that define them.
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