Physics:Quantum Commutator: Difference between revisions

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== References ==
== References ==
{{reflist|3}}
{{reflist|3}}
* {{Cite web |title=Commutator |url=https://mathworld.wolfram.com/Commutator.html |website=Wolfram MathWorld |access-date=2026-05-23}}
* {{Cite book |last=Griffiths |first=David J. |title=Introduction to Quantum Mechanics |edition=2nd |publisher=Prentice Hall |year=2004 |isbn=0-13-805326-X}}
* {{Cite book |last=Dirac |first=P. A. M. |title=The Principles of Quantum Mechanics |publisher=Oxford University Press |year=1930}}
* {{Cite book |last=Liboff |first=Richard L. |title=Introductory Quantum Mechanics |edition=4th |publisher=Addison-Wesley |year=2003 |isbn=0-8053-8714-5}}
* {{Cite book |last=McMahon |first=David |title=Quantum Field Theory |publisher=McGraw Hill |year=2008 |isbn=978-0-07-154382-8}}


{{Author|Harold Foppele}}
{{Author|Harold Foppele}}

Revision as of 22:03, 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

Full contents

References

  • Griffiths, David J. (2004). Introduction to Quantum Mechanics (2nd ed.). Prentice Hall. ISBN 0-13-805326-X. 
  • Liboff, Richard L. (2003). Introductory Quantum Mechanics (4th ed.). Addison-Wesley. ISBN 0-8053-8714-5. 
  • McMahon, David (2008). Quantum Field Theory. McGraw Hill. ISBN 978-0-07-154382-8. 


Author: Harold Foppele


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