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.