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# Coulomb operator

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 Title: Coulomb operator Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### 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.