Physics:Quantum Observables and operators - Revision history

WikiHarold: Restore missing Quantum reference definitions

2026-05-24T00:31:20Z

Restore missing Quantum reference definitions

← Older revision		Revision as of 00:31, 24 May 2026
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	* <math>\|\psi\rangle</math> is the eigenstate		* <math>\|\psi\rangle</math> is the eigenstate

	After measurement, the system collapses into the corresponding eigenstate.<ref name="SakuraiQM" />		After measurement, the system collapses into the corresponding eigenstate.<ref name="SakuraiQM">{{cite book
			\|last=Sakurai
			\|first=J. J.
			\|title=Modern Quantum Mechanics
			\|publisher=Addison-Wesley
			\|year=1994
			\|isbn=978-0201539295
			}}</ref>

	== Expectation values ==		== Expectation values ==
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	<math>\langle A \rangle = \int \psi^*(x), \hat{A}, \psi(x), dx</math>		<math>\langle A \rangle = \int \psi^*(x), \hat{A}, \psi(x), dx</math>

	This connects the operator formalism to experimentally observable averages.<ref name="GriffithsQM" />		This connects the operator formalism to experimentally observable averages.<ref name="GriffithsQM">{{cite book
			\|last=Griffiths
			\|first=David J.
			\|title=Introduction to Quantum Mechanics
			\|edition=2nd
			\|publisher=Pearson
			\|year=2005
			\|isbn=978-0131118928
			}}</ref>

	== Commutation relations ==		== Commutation relations ==
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	{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

	=References=		= References =
	{{reflist\|3}}		{{reflist\|3}}
	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

	{{Sourceattribution\|Physics:Quantum Observables and operators\|1}}		{{Sourceattribution\|Physics:Quantum Observables and operators\|1}}

Maintenance script: Normalize quantum page header order

2026-05-22T11:30:57Z

Normalize quantum page header order

← Older revision		Revision as of 11:30, 22 May 2026
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	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}
	{{Quantum article nav\|previous=Physics:Quantum Hilbert space\|previous label=Hilbert space\|next=Physics:Quantum mechanics\|next label=Mechanics}}		{{Quantum article nav\|previous=Physics:Quantum Hilbert space\|previous label=Hilbert space\|next=Physics:Quantum mechanics\|next label=Mechanics}}

	<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">

Maintenance script: Clean Book label remnants and backlink spacing

2026-05-22T11:09:14Z

Clean Book label remnants and backlink spacing

← Older revision		Revision as of 11:09, 22 May 2026
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	{{Short description\|Mathematical representation of measurable quantities in quantum mechanics using operators acting on state vectors}}		{{Short description\|Mathematical representation of measurable quantities in quantum mechanics using operators acting on state vectors}}

	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}
	{{Quantum article nav\|previous=Physics:Quantum Hilbert space\|previous label=Hilbert space\|next=Physics:Quantum mechanics\|next label=Mechanics}}		{{Quantum article nav\|previous=Physics:Quantum Hilbert space\|previous label=Hilbert space\|next=Physics:Quantum mechanics\|next label=Mechanics}}

Maintenance script: Remove hidden BOM characters and direct Book label after Short description

2026-05-22T11:01:26Z

Remove hidden BOM characters and direct Book label after Short description

← Older revision		Revision as of 11:01, 22 May 2026
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	{{Short description\|Mathematical representation of measurable quantities in quantum mechanics using operators acting on state vectors}}~~Book I~~		{{Short description\|Mathematical representation of measurable quantities in quantum mechanics using operators acting on state vectors}}

	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}

Maintenance script: Clean Short description prefix and add Book I label

2026-05-22T10:46:31Z

Clean Short description prefix and add Book I label

← Older revision		Revision as of 10:46, 22 May 2026
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	~~~~{{Short description\|Mathematical representation of measurable quantities in quantum mechanics using operators acting on state vectors}}		{{Short description\|Mathematical representation of measurable quantities in quantum mechanics using operators acting on state vectors}}Book I

	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}

Maintenance script: Add Foundations previous-next navigation

2026-05-20T12:15:11Z

Add Foundations previous-next navigation

← Older revision		Revision as of 12:15, 20 May 2026
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	{{Short description\|Mathematical representation of measurable quantities in quantum mechanics using operators acting on state vectors}}		{{Short description\|Mathematical representation of measurable quantities in quantum mechanics using operators acting on state vectors}}

	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}
			{{Quantum article nav\|previous=Physics:Quantum Hilbert space\|previous label=Hilbert space\|next=Physics:Quantum mechanics\|next label=Mechanics}}

	<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">

Maintenance script: Improve Book I intro quality

2026-05-20T09:02:22Z

Improve Book I intro quality

← Older revision		Revision as of 09:02, 20 May 2026
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	{{Short description\|Mathematical representation of measurable quantities in quantum mechanics using operators acting on state vectors}}		{{Short description\|Mathematical representation of measurable quantities in quantum mechanics using operators acting on state vectors}}

	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}
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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;">
	'''Observables and operators''' ~~is a Book I topic~~ in ~~the Quantum Collection. In~~ quantum mechanics, observables are physical quantities that can be measured, such as position, momentum, energy, and angular momentum~~. These quantities are represented mathematically by operators acting on the state of a system, typically described by a wavefunction \psi(x,t) or a state vector \|\psi\rangle~~. The operator formalism is central to quantum theory, replacing classical variables with linear operators on a Hilbert space. In quantum mechanics, observables are physical quantities that can be measured, such as position, momentum, energy, and angular momentum. ~~These quantities~~ are represented ~~mathematically by~~ operators ~~acting~~ on the ~~state of a~~ system~~, typically described by a wavefunction \psi(x,t) or a state vector \|\psi\rangle~~.~~{{cite book~~ The ~~operator formalism~~ is ~~central to quantum theory~~, ~~replacing classical variables with linear operators on a Hilbert space~~.		'''Observables and operators''' in quantum mechanics, observables are physical quantities that can be measured, such as position, momentum, energy, and angular momentum. The operator formalism is central to quantum theory, replacing classical variables with linear operators on a Hilbert space. In quantum mechanics, observables are physical quantities that can be measured, such as position, momentum, energy, and angular momentum. An operator is a mathematical object that acts on a function or state vector to produce another function. Operators are generally linear and may be represented as differential operators, matrices, or more abstract mappings depending on the system. The measurement postulate of quantum mechanics states that when an observable is measured, the result is one of the eigenvalues of the corresponding operator.
	</div>		</div>

Maintenance script: Clean Book I red links, intro, and image slots

2026-05-20T08:11:07Z

Clean Book I red links, intro, and image slots

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 {{Short description|Mathematical representation of measurable quantities in quantum mechanics using operators acting on state vectors}}
 {{Quantum book backlink|Foundations}}
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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;">
-In quantum mechanics, '''observables''' are physical quantities that can be measured, such as position, momentum, energy, and angular momentum. These quantities are represented mathematically by '''operators''' acting on the state of a system, typically described by a wavefunction <math>\psi(x,t)</math> or a state vector <math>|\psi\rangle</math>.<ref name="GriffithsQM">{{cite book
+'''Observables and operators''' is a Book I topic in the Quantum Collection. In quantum mechanics, observables are physical quantities that can be measured, such as position, momentum, energy, and angular momentum. These quantities are represented mathematically by operators acting on the state of a system, typically described by a wavefunction \psi(x,t) or a state vector |\psi\rangle. The operator formalism is central to quantum theory, replacing classical variables with linear operators on a Hilbert space. In quantum mechanics, observables are physical quantities that can be measured, such as position, momentum, energy, and angular momentum. These quantities are represented mathematically by operators acting on the state of a system, typically described by a wavefunction \psi(x,t) or a state vector |\psi\rangle.{{cite book The operator formalism is central to quantum theory, replacing classical variables with linear operators on a Hilbert space.
 </div>

Maintenance script: Normalize Book I Quantum page structure

2026-05-19T22:47:54Z

Normalize Book I Quantum page structure

← Older revision		Revision as of 22:47, 19 May 2026
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	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

	{{Sourceattribution\|Quantum Observables and operators\|1}}		{{Sourceattribution\|Physics:Quantum Observables and operators\|1}}

Harold: Arrange page top as TOC lead image columns

2026-05-17T13:16:01Z

Arrange page top as TOC lead image columns

← Older revision		Revision as of 13:16, 17 May 2026
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	{{Quantum book backlink\|Foundations}}		{{Quantum book backlink\|Foundations}}

			<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">

			<div style="width:280px;">
			__TOC__
			</div>

			<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	In quantum mechanics, '''observables''' are physical quantities that can be measured, such as position, momentum, energy, and angular momentum. These quantities are represented mathematically by '''operators''' acting on the state of a system, typically described by a wavefunction <math>\psi(x,t)</math> or a state vector <math>\|\psi\rangle</math>.<ref name="GriffithsQM">{{cite book		In quantum mechanics, '''observables''' are physical quantities that can be measured, such as position, momentum, energy, and angular momentum. These quantities are represented mathematically by '''operators''' acting on the state of a system, typically described by a wavefunction <math>\psi(x,t)</math> or a state vector <math>\|\psi\rangle</math>.<ref name="GriffithsQM">{{cite book
	\|last=Griffiths		\|last=Griffiths
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	The operator formalism is central to quantum theory, replacing classical variables with linear operators on a Hilbert space.		The operator formalism is central to quantum theory, replacing classical variables with linear operators on a Hilbert space.
	[[File:Quantum_operator_observable_yellow.jpg\|thumb\|~~400px~~\|Light-yellow schematic illustrating how quantum operators act on wavefunctions to yield measurable observables such as position, momentum, and energy.]]		</div>

			<div style="width:300px;">
			[[File:Quantum_operator_observable_yellow.jpg\|thumb\|280px\|Light-yellow schematic illustrating how quantum operators act on wavefunctions to yield measurable observables such as position, momentum, and energy.]]
			</div>

			</div>

	== Operators in quantum mechanics ==		== Operators in quantum mechanics ==