Physics:Quantum Matrix mechanics - Revision history

WikiHarold: Expand short Quantum intro

2026-05-23T22:58:57Z

Expand short Quantum intro

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	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	'''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 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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WikiHarold: Move Quantum references inline

2026-05-23T22:15:13Z

Move Quantum references inline

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	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	'''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.		'''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>
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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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	== References ==		== References ==
	{{reflist\|3}}		{{reflist\|3}}
	* {{Cite book \|last=Green \|first=Herbert S. \|title=Matrix Mechanics \|location=Groningen \|publisher=P. Noordhoff \|year=1965 \|asin=B0006BMIP8}}
	* {{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}}

WikiHarold: Replace Quantum references with Wikipedia-sourced references

2026-05-23T22:03:02Z

Replace Quantum references with Wikipedia-sourced references

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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}}

WikiHarold: Use Quantum See also index module

2026-05-23T21:57:44Z

Use Quantum See also index module

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	== See also ==		== See also ==
	* [[Physics:Quantum mechanics]]		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}
	* [[Physics:Quantum Commutator]]
	* [[Physics:~~Quantum Uncertainty principle]]~~
	* [[Physics:Quantum ~~Hamiltonian]]~~
	* quantum operators

	== References ==		== References ==

WikiHarold: Remove leading BOM from Quantum page

2026-05-23T21:55:37Z

Remove leading BOM from Quantum page

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	{{Short description\|Formulation of quantum mechanics using matrices}}		{{Short description\|Formulation of quantum mechanics using matrices}}
	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}
	{{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}}

WikiHarold: Repair Quantum page See also and references

2026-05-23T21:53:39Z

Repair Quantum page See also and references

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	{{Short description\|Formulation of quantum mechanics using matrices}}		{{Short description\|Formulation of quantum mechanics using matrices}}
	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}
	{{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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	* [[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.

	== ~~Related concepts~~ ==		== See also ==
	* [[Physics:Quantum mechanics]]		* [[Physics:Quantum mechanics]]
	* [[Physics:Quantum Commutator]]		* [[Physics:Quantum Commutator]]

WikiHarold: Restore Quantum article header layout

2026-05-23T21:41:44Z

Restore Quantum article header layout

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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}}

	~~[[File~~:~~Quantum_Matrix_mechanics_educational_yellow.png\|thumb\|right\|Matrix mechanics represents observables by arrays or operators whose order may matter.]]~~		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">

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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.		'''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>

			<div style="width:300px;">
			[[File:Quantum_Matrix_mechanics_educational_yellow.png\|thumb\|280px\|Matrix mechanics represents observables by arrays or operators whose order may matter.]]
			</div>

			</div>

	== Description ==		== Description ==

Maintenance script: Remove red links from related concepts

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Remove red links from related concepts

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	* [[Physics:Quantum Uncertainty principle]]		* [[Physics:Quantum Uncertainty principle]]
	* [[Physics:Quantum Hamiltonian]]		* [[Physics:Quantum Hamiltonian]]
	* ~~[[Physics:Quantum operator]]~~		* quantum operators

	== References ==		== References ==

Maintenance script: Replace red link with existing Schrodinger equation page

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Replace red link with existing Schrodinger equation page

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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 ~~Wave mechanics~~\|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]], but it remains a natural language for spin, finite-dimensional systems, quantum information, and operator methods.

	== Historical names ==		== Historical names ==

Maintenance script: Add navigation and educational image

2026-05-23T09:57:24Z

Add navigation and educational image

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	{{Short description\|Formulation of quantum mechanics using matrices}}		{{Short description\|Formulation of quantum mechanics using matrices}}
	{{Quantum book~~/methods~~ backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}
			{{Quantum article nav\|previous=Physics:Quantum Uncertainty principle\|previous label=Uncertainty principle\|next=Physics:Quantum Commutator\|next label=Commutator}}

			[[File:Quantum_Matrix_mechanics_educational_yellow.png\|thumb\|right\|Matrix mechanics represents observables by arrays or operators whose order may matter.]]

	'''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.		'''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.
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	Matrix mechanics was later shown to be equivalent to [[Physics:Quantum Wave mechanics\|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 Wave mechanics\|wave mechanics]], but it remains a natural language for spin, finite-dimensional systems, quantum information, and operator methods.

			== Historical names ==
			* [[Biography:Werner Heisenberg\|Werner Heisenberg]] introduced the first form of matrix mechanics.
			* [[Biography:Max Born\|Max Born]] and Pascual Jordan recognized and developed the matrix structure of the theory.

	== Related concepts ==		== Related concepts ==

← Older revision		Revision as of 22:03, 23 May 2026
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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}}

← Older revision		Revision as of 21:55, 23 May 2026
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	{{Short description\|Formulation of quantum mechanics using matrices}}		{{Short description\|Formulation of quantum mechanics using matrices}}
	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}
	{{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}}

← Older revision		Revision as of 09:57, 23 May 2026
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	{{Short description\|Formulation of quantum mechanics using matrices}}		{{Short description\|Formulation of quantum mechanics using matrices}}
	{{Quantum book~~/methods~~ backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}
			{{Quantum article nav\|previous=Physics:Quantum Uncertainty principle\|previous label=Uncertainty principle\|next=Physics:Quantum Commutator\|next label=Commutator}}

			[[File:Quantum_Matrix_mechanics_educational_yellow.png\|thumb\|right\|Matrix mechanics represents observables by arrays or operators whose order may matter.]]

	'''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.		'''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.
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	Matrix mechanics was later shown to be equivalent to [[Physics:Quantum Wave mechanics\|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 Wave mechanics\|wave mechanics]], but it remains a natural language for spin, finite-dimensional systems, quantum information, and operator methods.

			== Historical names ==
			* [[Biography:Werner Heisenberg\|Werner Heisenberg]] introduced the first form of matrix mechanics.
			* [[Biography:Max Born\|Max Born]] and Pascual Jordan recognized and developed the matrix structure of the theory.

	== Related concepts ==		== Related concepts ==