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== See also ==
== See also ==
* [[Physics:Quantum mechanics]]
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}
* [[Physics:Quantum Matrix mechanics]]
* [[Physics:Quantum Uncertainty principle]]
* quantum operators
* quantum observables


== References ==
== References ==

Revision as of 21:57, 23 May 2026

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In quantum mechanics, a commutator measures how much two operators fail to commute. For two operators A and B, the commutator is

[A,B]=AB−BA.

A commutator compares doing two quantum operations in different orders.

Role in quantum mechanics

Commutators are central because quantum observables are represented by operators. If two observables have a nonzero commutator, the corresponding quantities generally cannot both have sharply defined values in the same state.

The canonical position and momentum commutator is

[x,p]=iℏI.

This relation underlies the uncertainty principle and is one of the basic structures of matrix mechanics.

See also

Table of contents (217 articles)

Index

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References


Author: Harold Foppele


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