Simply write down the time-independent Schroedinger equation for electrons contained in e.g., a carbon atom.

Fix the nucleus at some point in space for simplicity.

You may solve it numerically.

But you must take the all combinations of inter-electronic Coulomb repulsion terms +q^2/ABS(Ri-Rj) into your calculation explicitly absolutely.

Now calculate the solution in an ab initio way. Do not introduce and assume any orbital notion from the start.

Treat all electrons equally.

Then do you think your calculation will yield the solution that has similar features with the prevailing atomic theory?

Will your solution have the shell structure?

Will your solution have the exclusion feature?

Will the exclusion property between electrons appear naturally in your solution?

A Pithecantropus Japonicus who is engraving the Schroedinger equation on the wall of a cave he is living

July 31, 2013