Exchange operator

The Exchange operator, 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:

$hat\; K\_j\; (1)\; f(1)=\; varphi\_j(1)\; int\; \{\; frac\{varphi\_j^*(2)f(2)\}\{r\_\{12dv\_2\}$

where $hat\; K\_j\; (1)$ is the one-electron exchange operator,

$f(1),\; f(2)$ are the one-electron wavefunction being acted upon by the Exchange operator as functions of the positions of electron 1 and electron 2,

$phi\_j(1),\; phi\_j(2)$ are the one-electron wavefunction of the j-th electron as functions of the positions of electron 1 and electron 2,

$r\_\{12\}$ is the distance between electrons 1 and 2.

In Quantum Physics the Exchange Operator can be thought of as a Hermitian operator which swaps the labels on any two identical particles.

ee also

*Core Hamiltonian

*Coulomb operator