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:


 * $$ \widehat J_j (1) f_i(1)= f_i(1) \int { \left | \varphi_j(2) \right | }^2 \frac{1}{r_{12}}\,dr_2 $$

where


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


 * $$ f_i(1) $$ is the one-electron wavefunction of the $$ i^{th} $$ electron being acted upon by the Coulomb operator,


 * $$\varphi_j(2)$$ is the one-electron wavefunction of the $$ j^{th} $$ electron,


 * $$r_{ij}$$ is the distance between electrons $$ (i) $$ and $$ (j) $$.