Physics:Quantum Commutator
In quantum mechanics, a commutator measures how much two operators fail to commute. For two operators and , the commutator is
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
This relation underlies the uncertainty principle and is one of the basic structures of matrix mechanics.
See also
Table of contents (217 articles)
Index
Core theory
Applications and extensions
Full contents
1. Foundations (14) Back to index
2. Conceptual and interpretations (14) Back to index
3. Mathematical structure and systems (15) Back to index
4. Atomic and spectroscopy (14) Back to index
5. Wavefunctions and modes (9) Back to index
6. Quantum dynamics and evolution (21) Back to index
7. Measurement and information (9) Back to index
8. Quantum information and computing (15) Back to index
102. Physics:Quantum BB84
9. Quantum optics and experiments (10) Back to index
10. Open quantum systems (15) Back to index
11. Quantum field theory (23) Back to index
12. Statistical mechanics and kinetic theory (9) Back to index
13. Condensed matter and solid-state physics (17) Back to index
181. Physics:Quantum well
186. Physics:Quantum dot
14. Plasma and fusion physics (8) Back to index
15. Timeline (8) Back to index
16. Advanced and frontier topics (16) Back to index
References
- "Commutator". https://mathworld.wolfram.com/Commutator.html.
- Dirac, P. A. M. (1930). The Principles of Quantum Mechanics. Oxford University Press.
Author: Harold Foppele