# Coulomb operator

The Coulomb operator, named after Charles-Augustin de Coulomb, is a quantum mechanical operator used in the field of quantum chemistry. Specifically, it is a term found in the Fock operator. It is defined as:

$\widehat J_j (1) f(1)= f(1) \int { \left | \varphi_j(2) \right | }^2 \frac{1}{r_{12}}\,dv_2$

where

$\widehat J_j (1)$ is the one-electron Coulomb operator defining the repulsion resulting from electron j,

f(1) is a one-electron wavefunction being acted upon by the Coulomb operator,

$\varphi_j(2)$ is the one-electron wavefunction of the jth electron,

$r_{12}$ is the distance between electrons 1 and 2.