Particle in a Box 1 (from Dr. Liebman): You will remember that the energy of a particle in a 3 (and 2) dimensional box is defined by 3 (or 2) quantum numbers. This brings up the concept of degeneracy: a particle with quantum numbers nx, ny, and nz = 3, 3, and 3 has the same energy as a particle with quantum numbers nx, ny, and nz = 1, 1, and 5, etc. etc. The question comes up whether or not there are any patterns to the degeneracy (Does this only happen with odd numbers? Are there certain patterns of odd numbers that give rise to degeneracy, etc.? ). Computers can, of course, compute a set of energy levels very quickly. Can you create a pattern-recognition algorithm to identify degeneracy patterns? It would also be nice to display, on a GUI, the pattern and show the user (i.e. a p-chem student) what

this degeneracy pattern is. (N.B. - Dr. Liebman has indicated that identifying such patterns in degeneracy may be a publishable piece of work!)