Exchange interaction

An effect with no classical counterpart, arising because identical electrons cannot be told apart even when they swap places. It underlies the chemical bond and magnetism.

In quantum mechanics electrons wear no name tags: swap two of them and nothing distinguishes the result. In 1926 Heisenberg used this to explain why helium's spectral lines fall into two separate families^[1]. Dirac reached the same idea the same year.

In 1927 Walter Heitler and Fritz London showed that when the exchange of the two electrons in a hydrogen molecule is included, the atoms attract or repel depending on how the spins point^[2]. The integral that measures the size of this effect is the exchange integral, which Yoshikatsu Sugiura calculated for each distance between the nuclei the same year.

In 1928 Heisenberg used the same effect to explain why electron spins line up in iron and similar materials, turning the whole piece into a magnet^[3]. The electric force at work is the same as in classical physics; it is the quantum fact that electrons cannot be told apart that produces an entirely new effect.