Quantum Mechanics Solution Manual |
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© Leon van Dommelen |
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3.5.8.3 Solution pipeg-c
Question:
Shade the regions where the particle is likely to be found in the energy eigenstate.
Answer:
The wave function is
Now the trick is to realize that the wave function is zero when any of the three sines is zero. Looking along the -direction, you will see an array of 3 times 2 blobs, or 6 blobs:
Figure 3.2:
Eigenstate .
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The white horizontal centerline line along the pipe corresponds to being zero at , and the two white vertical white lines correspond to being zero at and . The factor in the wave function will split it further into six blobs front and 6 blobs rear, but that is not visible when looking along the -direction; the front blobs cover the rear ones. Seen from the top, you would again see an array of 3 times 2 blobs, the top blobs hiding the bottom ones.