In quantum mechanics, and in particular in quantum chemistry, the electronic density $\backslash rho$ corresponding to an N-electron wavefunction $\backslash Psi^\{(N)\}$ 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 $\backslash Psi^\{(N)\}$ is a Slater determinant made of N spin orbitals $\backslash varphi\_k$:

$$

\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.

Atomic physics | Quantum chemistry