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== References ==
== References ==
{{reflist|3}}
{{reflist|3}}
* {{Cite journal |last=Heisenberg |first=W. |title=Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen |journal=Zeitschrift für Physik |year=1925 |volume=33 |pages=879-893 |doi=10.1007/BF01328377}}
* {{Cite book |last=Green |first=Herbert S. |title=Matrix Mechanics |location=Groningen |publisher=P. Noordhoff |year=1965 |asin=B0006BMIP8}}
* {{Cite web |title=Matrix mechanics |url=https://www.britannica.com/science/matrix-mechanics |website=Encyclopaedia Britannica |access-date=2026-05-23}}
* {{Cite journal |last=Heisenberg |first=Werner |title=Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen |journal=Zeitschrift für Physik |year=1925 |volume=33 |pages=879-893 |doi=10.1007/BF01328377}}
* {{Cite journal |last=Pauli |first=Wolfgang |title=Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik |journal=Zeitschrift für Physik |year=1926 |volume=36 |issue=5 |pages=336-363 |doi=10.1007/BF01450175}}
* {{Cite book |last=Dirac |first=Paul A. M. |title=The Principles of Quantum Mechanics |edition=4th revised |location=New York |publisher=Oxford University Press |year=1981 |isbn=0-19-852011-5}}


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

Revision as of 22:03, 23 May 2026

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Matrix mechanics is a formulation of quantum mechanics in which physical quantities are represented by matrices or operators. It was developed by Werner Heisenberg, Max Born, and Pascual Jordan in 1925.

Matrix mechanics represents observables by arrays or operators whose order may matter.

Description

In matrix mechanics, observables such as position, momentum, and energy are represented by mathematical objects that do not always commute. The order of multiplication can matter:

AB≠BA

This non-commutative structure is one of the mathematical roots of the uncertainty principle.

Matrix mechanics was later shown to be equivalent to wave mechanics, but it remains a natural language for spin, finite-dimensional systems, quantum information, and operator methods.

Historical names

  • Werner Heisenberg introduced the first form of matrix mechanics.
  • Max Born and Pascual Jordan recognized and developed the matrix structure of the theory.

See also

Table of contents (217 articles)

Index

Full contents

References

  • Green, Herbert S. (1965). Matrix Mechanics. Groningen: P. Noordhoff. 
  • Heisenberg, Werner (1925). "Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen". Zeitschrift für Physik 33: 879-893. doi:10.1007/BF01328377. 
  • Pauli, Wolfgang (1926). "Über das Wasserstoffspektrum vom Standpunkt der neuen Quantenmechanik". Zeitschrift für Physik 36 (5): 336-363. doi:10.1007/BF01450175. 
  • Dirac, Paul A. M. (1981). The Principles of Quantum Mechanics (4th revised ed.). New York: Oxford University Press. ISBN 0-19-852011-5. 


Author: Harold Foppele


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