Commutator
A mathematical operator evaluating whether two quantum mechanical operators commute with one another.
Governing formula
[Â, B̂] = Â B̂ - B̂ Â
SI unit
Product Unit of  and B̂
In depth
If two operators commute ([Â, B̂] = 0), they share a common set of eigenfunctions, allowing both observables to be measured simultaneously with exact precision. If non-zero (like [x̂, p̂] = i ℏ), the observables exhibit a Heisenberg uncertainty relationship.
Examples in the real world
Proving position and momentum do not commute ([x̂, p̂] = i ℏ), establishing the Heisenberg uncertainty principle.