Exchange interaction

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Exchange interaction is the quantum mechanical effect of increasing or decreasing the energy of two or more fermions when their wave functions overlap. This energy change is the result of an effect due to the identity of particles and exchange symmetry.

For example, any two electrons in the universe are considered indistinguishable particles, and so according to quantum mechanics in 3 dimensions, every particle must behave as a boson or a fermion. In the former case, two (or more) particles can occupy the same quantum state and this results in a lack of exchange interaction between them; in the latter case, the particles can not occupy the same state according to the Pauli exclusion principle. From Quantum field theory, the spin-statistics theorem demands that all particles with half-integer spin behave as fermions and all particles with integer spin behave as bosons. Thus, it so happens that all electrons are fermions, since they have spin 1/2.

As a mathematical consequence, fermions exhibit strong repulsion when their wave function overlap, but bosons do not. This repulsion is what the exchange interaction models. Fermi repulsion results in "stiffness" of fermions. That is why atomic matter, is "stiff" or "rigid" to touch. Where wave functions of electrons overlap, Pauli repulsion takes place. The same is true for protons and neutrons where due to their larger mass, the rigidity of baryons is much larger than that of electrons.