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to 1-D systems.
- Ahead to the classical harmonic oscillator.
- Back to the Index.
- Copyright 1999, 2000 John S. Winn. All rights reserved. Last updated September 8, 2000.
- Ahead to the classical harmonic oscillator.
For systems moving in more than one dimension, symmetry plays
a very important role, especially in the pattern of energy levels.
This page supplements the 3-D discussion that opens Section 12.3
on page 409.
The top two graphs show the two-dimensional wavefunction as a
3D graph on the left and as a contour diagram superimposed on
a "top" view of the wavefunction. The middle two graphs
show the same thing for the square of the wavefunction.
The bottom graph plots the energy level scheme for the lowest
few energies. The levels are sorted left to right by the nx quantum
number, and each stack has ny varying from 1 on up.
You can change the two quantum numbers as well as the size of
the box (through the Lx and Ly values). Look for symmetry changes
in the wavefunction and degeneracy changes in the energy level
pattern as you change these numbers.
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