  In light of the recent work by Sahni et al., Harbola, and Gaudoin and Burke,
the question of mapping from an excited-state density of a many-electron
interacting system to the potential of the related non-interacting system is
analyzed. To do so, we investigate the Levy-Nagy criterion quantitatively for
several excited-states. Our work indicates that Levy-Nagy criterion may fix the
density to potential map uniquely.
