Structure Theory Appproximate the solutions of the Schrödinger equation ˆ HΨ = EΨ E [Ψ] = Ψ ˆ H Ψ as a functional of the One-Body Reduced Density Matrix E [γ] = ˆ Hγ where the Density Matrix is defined as γ (x1 , x1 ) = N dx2...N Ψ(x1 , x2 , . . . , xN )Ψ∗(x1 , x2 , . . . , xN ) 2