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:
where is the one-electron exchange operator,
are the one-electron wavefunction being acted upon by the Exchange operator as functions of the positions of electron 1 and electron 2,
are the one-electron wavefunction of the j-th electron as functions of the positions of electron 1 and electron 2,
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.
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