ELECTRONIC DENSITY

In quantum mechanics, and in particular in quantum chemistry, the 'electronic density' $$
ho corresponding to an ''N''-electron wavefunction $Psi^\{(N)\}$ is the one-electron function given by
:$$
ho(x)=int dx_2 ... dx_N |Psi^{(N)}(x,x_2,...,x_N)|^2

In the case $Psi^\{(N)\}$ is a Slater determinant made of ''N'' spin orbitals :
:$$
ho(x)={1 over N}sum_{k=1}^N |arphi_k(x)|^2

The 'two-electron electronic density' is given by
:$$
ho(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.