The effect of cusps in time-dependent quantum mechanics
  Spatial cusps in initial wavefunctions can lead to non-analytic behavior in time. We suggest a method for calculating the short-time behavior in such situations. For these cases, the density does not match its Taylor-expansion in time, but the Runge-Gross proof of time-dependent density functional theory still holds, as it requires only the potential to be time-analytic. 
Zeng-hui Yang, Neepa T. Maitra, Kieron Burke
quant-ph cond-mat.mtrl-sci cond-mat.other physics.atom-ph