Electronic density

In quantum mechanics, and in particular in quantum chemistry, the electronic density ρ corresponding to an N-electron wavefunction Ψ^(N) is the one-electron function given by

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In the case Ψ^(N) is a Slater determinant made of N spin orbitals :

The two-electron electronic density is given by

Those quantities are particularly important in the context of density functional theory.

The coordinates x used here are the spin-spatial coordinates.