Exchange operator

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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:

$\hat K_j (1) f(1)= \varphi_j(1) \int { \frac{\varphi_j^*(2)f(2)}{r_{12}}dv_2}$

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,

$φ j (1),φ j (2)$ 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.