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:

${\displaystyle {\widehat {J}}_{j}(1)f(1)=f(1)\int {\left|\varphi _{j}(2)\right|}^{2}{\frac {1}{r_{12}}}\,dr_{2}}$

where

${\displaystyle {\widehat {J}}_{j}(1)}$ 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,

${\displaystyle \varphi _{j}(2)}$ is the one-electron wavefunction of the jth electron,

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

See also

• Core Hamiltonian
• Exchange operator