Coulomb operator explained

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:^[1]

\widehat J _{j} ( 1 ) f _{i(1)=} f _{i(1)} \int { \left | \varphi _{j(2)} \right | } ^{2} (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) .

See also

• Core Hamiltonian
• Exchange operator

Notes and References

1. Book: Ramachandran, K. I. . Computational chemistry and molecular modeling : principles and applications . 2008 . Springer . G. Deepa, K. Namboori . 978-3-540-77304-7 . Berlin . 107 . 272298712.