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:

${\widehat {J}}_{j}(1)f_{i}(1)=f_{i}(1)\int {\left|\varphi _{j}(1)\right|}^{2}{\frac {1}{r_{ij}}}\,dr_{j}$

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,

$\varphi _{j}(1)$ is the one-electron wavefunction of the $j^{th}$ electron,

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

See also

• Core Hamiltonian
• Exchange operator