Metrics for Two Electron Random Potential Systems

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.