  Metrics have been used to investigate the relationship between wavefunction
distances and density distances for families of specific systems. We extend
this research to look at random potentials for time-dependent single electron
systems, and for ground-state two electron systems. We find that Fourier series
are a good basis for generating random potentials. These random potentials also
yield quasi-linear relationships between the distances of ground-state
densities and wavefunctions, providing a framework in which Density Functional
Theory can be explored.
