Physics:Quantum methods/quantization - Revision history

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	~~{{Quantum article nav\|previous=Physics:Quantum methods/field theory\|previous label=Field theory\|next=Physics:Quantum methods/renormalization\|next label=Renormalization}}~~



	{{Short description\|Procedure of constructing a quantum theory from a classical system}}		{{Short description\|Procedure of constructing a quantum theory from a classical system}}
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	{{Short description\|Procedure of constructing a quantum theory from a classical system}}II		{{Short description\|Procedure of constructing a quantum theory from a classical system}}
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	{{Short description\|Procedure of constructing a quantum theory from a classical system}}~~Book III~~		{{Short description\|Procedure of constructing a quantum theory from a classical system}}II
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	{{Short description\|Procedure of constructing a quantum theory from a classical system}}		{{Short description\|Procedure of constructing a quantum theory from a classical system}}Book III
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	{{Short description\|Procedure of constructing a quantum theory from a classical system}}		{{Short description\|Procedure of constructing a quantum theory from a classical system}}

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	{{Short description\|Procedure of constructing a quantum theory from a classical system}}		{{Short description\|Procedure of constructing a quantum theory from a classical system}}
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	{{Short description\|Procedure of constructing a quantum theory from a classical system}}		{{Short description\|Procedure of constructing a quantum theory from a classical system}}
	{{Quantum methods backlink\|Field and many-body methods}}		{{Quantum methods backlink\|Field and many-body methods}}

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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;">
	'''~~Quantization~~''' is the procedure of constructing a ~~[[quantum mechanics\|~~quantum theory]] from a corresponding ~~[[classical mechanics\|~~classical system]]. It provides the bridge between classical descriptions of physical systems and their quantum counterparts.		'''quantization''' is a method or tool used in quantum physics. Quantization is the procedure of constructing a quantum theory from a corresponding classical system. It provides the bridge between classical descriptions of physical systems and their quantum counterparts. Overview of key concepts in quantum field theory Quantization is the procedure of constructing a quantum theory from a corresponding classical system. It provides the bridge between classical descriptions of physical systems and their quantum counterparts. In classical physics, physical quantities such as position and momentum are represented by numbers. In quantum theory, they are represented by operators acting on a Hilbert space. The fundamental rule of canonical quantization replaces classical Poisson brackets with commutators: * Canonical quantization – promotes classical variables to operators * Path integral quantization – sums over all possible histories * Second quantization – describes systems with variable particle number Quantization underlies quantum field theory, many-body theory, and modern particle physics.</div>

	~~<div style="float:right; border:1px solid #ccc; padding:4px; background:#fff8dc; margin:0 0 1em 1em; width:420px;">~~
	~~<div style="font-size:90%;">~~Overview of key concepts in quantum field theory</div>
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	== Overview ==		== Overview ==
	In classical physics, physical quantities such as position and momentum are represented by numbers. In quantum theory, they are represented by ~~[[operator]]s~~ acting on a [[Hilbert space]].		In classical physics, physical quantities such as position and momentum are represented by numbers. In quantum theory, they are represented by operators acting on a [[Physics:Quantum Hilbert space\|Hilbert space]].

	The fundamental rule of canonical quantization replaces classical [[Poisson ~~bracket]]s~~ with commutators:		The fundamental rule of canonical quantization replaces classical Poisson brackets with commutators:
	<math>[x, p] = i\hbar</math>		<math>[x, p] = i\hbar</math>

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	== Applications ==		== Applications ==
	Quantization underlies [[quantum field theory]], [[many-body theory]], and modern particle physics.		Quantization underlies [[Physics:Quantum field theory\|quantum field theory]], many-body theory, and modern particle physics.

	== Description ==		== Description ==

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	== Applications ==		== Applications ==
	Quantization underlies [[quantum field theory]], [[many-body theory]], and modern particle physics.		Quantization underlies [[quantum field theory]], [[many-body theory]], and modern particle physics.

			== Description ==
			'''quantization''' is a method or conceptual tool used to formulate, calculate, measure, or interpret quantum systems. In the Quantum Collection it is treated as part of the practical vocabulary that connects mathematical formalism with experiments, simulation, and data analysis.

			== Use in quantum work ==
			The method helps define how states, observables, transformations, or measurement outcomes are represented. It is often used together with Hilbert-space notation, operators, probability amplitudes, and uncertainty estimates, depending on the problem being studied.

			== Connections ==
			quantization connects to the broader structure of [[Physics:Quantum mechanics\|quantum mechanics]], [[Physics:Quantum Measurement theory\|measurement theory]], and, where applicable, [[Physics:Quantum information theory\|quantum information theory]]. It is useful as a bridge between abstract formalism and concrete calculations.<ref name="qm-methods">{{cite web \|url=https://en.wikipedia.org/wiki/Quantum_mechanics \|title=Quantum mechanics \|website=Wikipedia \|access-date=2026-05-20}}</ref>

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

	== References ==		== References ==
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	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}
	{{Sourceattribution\|Physics:Quantum ~~Quantization~~\|1}}		{{Sourceattribution\|Physics:Quantum methods/quantization\|1}}

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	{{Short description\|Procedure of constructing a quantum theory from a classical system}}		{{Short description\|Procedure of constructing a quantum theory from a classical system}}Book III
	{{Quantum methods backlink\|Field and many-body methods}}		{{Quantum methods backlink\|Field and many-body methods}}

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