A commutator is an operator used in quantum mechanics to measure the extent to which two observables fail to commute, essentially defined as the difference between the product of two operators applied in different orders. Commutators play a crucial role in understanding the behavior of quantum systems, as they relate directly to the properties of observables and the uncertainty principle. The mathematical expression for a commutator of two operators, A and B, is given by [A, B] = AB - BA.
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