Kohn-Sham equations in density functional theory use an auxiliary one-electron Hamiltonian whose effective potential depends on the density. Its orbitals construct a density representing an interacting electronic system; this is distinct from explicitly diagonalizing a large many-electron determinant Hamiltonian.[ref]
Self-Consistent Equations Including Exchange and Correlation Effects by Walter Kohn and Lu Jeu Sham. 1965, pp. A1133–A1135, ground-state effective one-electron formulation
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