Here we consider adding two electrons to two "atoms," represented as finite wells,...

Here we consider adding two electrons to two "atoms," represented as finite wells, and investigate when the exclusion principle must be taken into account. In the accompanying figure, diagram (a) shows the four lowest-energy wave functions for a double finite well that represents atoms close together. To yield the lowest energy, the first electron added to this system must have wave function A and is shared equally between the atoms. The second would also have function A and be equally shared, but it would have to be opposite spin. A third would have function B. Now consider atoms far apart. As diagram (b) shows, the bumps do not extend much beyond the atoms—they don't

a.

b.

overlap—and functions A and B approach equal energy, as do functions C and D. Wave functions A and B in diagram (b) describe essentially identical shapes in the right well, while being opposite in the left well. Because they are of equal energy, sums or differences of A and B are now a valid alternative. An electron in a sum or difference would have the same energy as in either alone, so it would be just as "happy" in A, B, A + B, or A — B. Argue that in this spread-out situation, electrons can be put in one atom without violating the exclusion principle, no matter what states electrons occupy in the other atom