![]() when S = 1 the spatially antisymmetric/spin-triplet state). one with two electrons), one may attempt to model the state of each electron by first assuming the electrons behave independently, and taking wave functions in position space of Φ a ( r 1 ) has the characteristic value +1/4 (i.e. Taking a hydrogen molecule-like system (i.e. First, however, exchange will be explained with the neglect of spin. interchanged with respect to both spatial and spin coordinates. This means that the overall wave function of a system must be antisymmetric when two electrons are exchanged, i.e. Since electrons have spin 1/2, they are fermions. Multiple bosons may occupy the same quantum state however, by the Pauli exclusion principle, no two fermions can occupy the same state. The spin–statistics theorem of quantum field theory demands that all particles with half-integer spin behave as fermions and all particles with integer spin behave as bosons. Quantum mechanical particles are classified as bosons or fermions. Īlthough sometimes erroneously described as a force, the exchange interaction is a purely quantum mechanical effect unlike other forces.Įxchange interactions between localized electron magnetic moments However, it is not a true force and should not be confused with the exchange forces produced by the exchange of force carriers, such as the electromagnetic force produced between two electrons by the exchange of a photon, or the strong force between two quarks produced by the exchange of a gluon. The exchange interaction is sometimes called the exchange force. It has no classical analogue.Įxchange interaction effects were discovered independently by physicists Werner Heisenberg and Paul Dirac in 1926.įor interaction mediation by exchange of particles, see force carrier. Among other consequences, the exchange interaction is responsible for ferromagnetism and the volume of matter. This interaction increases (for fermions) or decreases (for bosons) the expectation value of the distance between identical particles (compared to distinguishable particles). The exchange interaction alters the expectation value of the distance when the wave functions of two or more indistinguishable particles overlap. For bosons, the exchange interaction takes the form of an effective attraction that causes identical particles to be found closer together, as in Bose–Einstein condensation. For fermions, this interaction is sometimes called Pauli repulsion and is related to the Pauli exclusion principle. Both bosons and fermions can experience the exchange interaction. ![]() The effect is due to the wave function of indistinguishable particles being subject to exchange symmetry, that is, either remaining unchanged (symmetric) or changing sign (antisymmetric) when two particles are exchanged. Despite sometimes being called an exchange force in an analogy to classical force, it is not a true force as it lacks a force carrier. In chemistry and physics, the exchange interaction or exchange splitting (with an exchange energy and exchange term) is a quantum mechanical effect that only occurs between identical particles. ![]()
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