In a recent Physical Review Letter, grad Zenghui Yang created a new mathematical procedure for studying the effects of cusps in quantum mechanics.

The figure shows a simple one-dimensional example of what happens to a wavefunction if the nucleus of an atom vanishes.  A similar behavior occurs for any atom, molecule, or solid when a time-dependent electric field is turned on.  Zenghui's new procedure makes it possible to calculate
the non-analytic behavior caused by a nuclear cusp.  These effects play a crucial role in the fundamental theorems of time-dependent density functional theory.