Periodic Table, chemical bonding, etc

As we discussed today, the periodic table originated from considerations of bonding, with elements arranged under elements with similar bonding behavior. With the development of quantum mechanics, and, specifically, considerations associated with the degeneracy and angular momentum patterns of one-electron states which are solutions to the Schrodinger equation for hydrogenic atoms (-1/r potential), there is a theoretical basis for understanding the periodic table.

In your assignment, you are asked to explore and establish the nature of the periodic table for harmonic oscillator potentials in 2 dimensions (and 3 dimensions as well if you can). Create a periodic table which might be appropriate for a HO type potential (r^2). Compare and contrast that to the periodic table for -1/r.

Aside from the central issue of the difference in the nature of the periodic table (if they are different), one could also address related intriguing issues such as: How do the degeneracy patterns different? Where do these degeneracies come from? (Why are states of different angular momentum sometimes degenerate?)...