Based on a computational procedure for determining the functional derivative with respect\nto the density of any antisymmetric N-particle wave function for a non-interacting system that leads\nto the density, we devise a test as to whether or not a wave function known to lead to a given density\ncorresponds to a solution of a Schr�¶dinger equation for some potential. We examine explicitly the\ncase of non-interacting systems described by Slater determinants. Numerical examples for the cases\nof a one-dimensional square-well potential with infinite walls and the harmonic oscillator potential\nillustrate the formalism.
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