impossiblewizardry | (no subject)

there's a lot more to say about the wavefunctinos of molecules than that they solve the schrodinger equation. Any quantum system solves the schrodinger equation; molecules are a subset of potentials and you can ask what's distinctive about them.

Here's something. For a molecule with n atoms, the electron density has O(n) critical points.

This is in the first chapter or two of Bader's book. There's generally a critical point at every nucleus, a critical point at every bond, a critical point in the middle of every ring. And then for molecules with cages like cubane, there's a critical point in the middle of the cage. Generally. This is not always the case, but it's pretty much always the case.

That's a limited number of critical points. I mean, I'm sure that the space of possible wavefunctions includes electron densities with arbitrarily high densities of critical points. So this is a very special smoothness property and so epxpansions in the density of critical points or something should allow you to speak very generally about molecules, but say something that's new, something that doesn't just follow from the schrodinger equation.

If this is a standard thing link me to the wikipedia article plz.