Domains of time-dependent density-potential mappings
  The key element in time-dependent density functional theory is the one-to-one correspondence between the one-particle density and the external potential. In most approaches this mapping is transformed into a certain type of Sturm-Liouville problem. Here we give conditions for existence and uniqueness of solutions and construct the weighted Sobolev space they lie in. As a result the class of v-representable densities is considerably widened with respect to previous work. 
Markus Penz and Michael Ruggenthaler
math-ph cond-mat.mtrl-sci math.MP physics.atom-ph quant-ph