Exchange interaction

In chemistry and physics, the exchange interaction is a quantum mechanical constraint on the states of indistinguishable particles. While sometimes called an exchange force, or, in the case of fermions, Pauli repulsion, its consequences cannot always be predicted based on classical ideas of force.^[1] Both bosons and fermions can experience the exchange interaction.

The wave function of indistinguishable particles is subject to exchange symmetry: the wave function either changes sign (for fermions) or remains unchanged (for bosons) when two particles are exchanged. The exchange symmetry alters the expectation value of the distance between two indistinguishable particles when their wave functions overlap. For fermions the expectation value of the distance increases, and for bosons it decreases (compared to distinguishable particles).^[2]

The exchange interaction arises from the combination of exchange symmetry and the Coulomb interaction. For an electron in an electron gas, the exchange symmetry creates an "exchange hole" in its vicinity, which other electrons with the same spin tend to avoid due to the Pauli exclusion principle. This decreases the energy associated with the Coulomb interactions between the electrons with same spin.^[3] Since two electrons with different spins are distinguishable from each other and not subject to the exchange symmetry, the effect tends to align the spins. Exchange interaction is the main physical effect responsible for ferromagnetism, and has no classical analogue.

For bosons, the exchange symmetry makes them bunch together, and the exchange interaction takes the form of an effective attraction that causes identical particles to be found closer together, as in Bose–Einstein condensation.

Exchange interaction effects were discovered independently by physicists Werner Heisenberg and Paul Dirac in 1926.^[4][5]