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# 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

$\rho(x)=\int \ dx_2 \ ... \ dx_N \ |\Psi^{(N)}(x,x_2,...,x_N)|^2$

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

$\rho(x)={1 \over N}\sum_{k=1}^N |\varphi_k(x)|^2$

The two-electron electronic density is given by

$\rho(x,x')=\int \ dx_3 \ ... \ dx_N \ |\Psi^{(N)}(x,x',x_3,...,x_N)|^2$

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

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