Physics:Quantum Matrix mechanics: Difference between revisions
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{{Quantum article nav|previous=Physics:Quantum Uncertainty principle|previous label=Uncertainty principle|next=Physics:Quantum Commutator|next label=Commutator}} | {{Quantum article nav|previous=Physics:Quantum Uncertainty principle|previous label=Uncertainty principle|next=Physics:Quantum Commutator|next label=Commutator}} | ||
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'''Matrix mechanics''' is a formulation of [[Physics:Quantum mechanics|quantum mechanics]] in which physical quantities are represented by matrices or operators. It was developed by [[Biography:Werner Heisenberg|Werner Heisenberg]], [[Biography:Max Born|Max Born]], and Pascual Jordan in 1925. | <div style="width:280px;"> | ||
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'''Matrix mechanics''' is a Book I topic in the Quantum Collection. '''Matrix mechanics''' is a formulation of [[Physics:Quantum mechanics|quantum mechanics]] in which physical quantities are represented by matrices or operators. It was developed by [[Biography:Werner Heisenberg|Werner Heisenberg]], [[Biography:Max Born|Max Born]], and Pascual Jordan in 1925.<ref>{{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}}</ref> Matrix mechanics is important because it made noncommuting observables the basic language of quantum theory. Instead of picturing electron orbits, it represents measurable quantities by arrays or operators whose multiplication order can matter. This formulation is equivalent to wave mechanics but remains especially natural for spin systems, finite-dimensional Hilbert spaces, and quantum information. | |||
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[[File:Quantum_Matrix_mechanics_educational_yellow.png|thumb|280px|Matrix mechanics represents observables by arrays or operators whose order may matter.]] | |||
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== Description == | == Description == | ||
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This non-commutative structure is one of the mathematical roots of the [[Physics:Quantum Uncertainty principle|uncertainty principle]]. | This non-commutative structure is one of the mathematical roots of the [[Physics:Quantum Uncertainty principle|uncertainty principle]]. | ||
Matrix mechanics was later shown to be equivalent to [[Physics:Quantum Schrödinger equation|wave mechanics]], but it remains a natural language for spin, finite-dimensional systems, quantum information, and operator methods. | Matrix mechanics was later shown to be equivalent to [[Physics:Quantum Schrödinger equation|wave mechanics]]<ref>{{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}}</ref>, but it remains a natural language for spin, finite-dimensional systems, quantum information, and operator methods. | ||
== Historical names == | == Historical names == | ||
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* [[Biography:Max Born|Max Born]] and Pascual Jordan recognized and developed the matrix structure of the theory. | * [[Biography:Max Born|Max Born]] and Pascual Jordan recognized and developed the matrix structure of the theory. | ||
== | == See also == | ||
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== References == | == References == | ||
{{reflist|3}} | {{reflist|3}} | ||
{{Author|Harold Foppele}} | {{Author|Harold Foppele}} | ||
Latest revision as of 22:58, 23 May 2026
Matrix mechanics is a Book I topic in the Quantum Collection. 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.[1] Matrix mechanics is important because it made noncommuting observables the basic language of quantum theory. Instead of picturing electron orbits, it represents measurable quantities by arrays or operators whose multiplication order can matter. This formulation is equivalent to wave mechanics but remains especially natural for spin systems, finite-dimensional Hilbert spaces, and quantum information.
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:
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[2], 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
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
- ↑ Heisenberg, Werner (1925). "Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen". Zeitschrift für Physik 33: 879-893. doi:10.1007/BF01328377.
- ↑ 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