Physics:Quantum Normal modes and field quantization - Revision history

WikiHarold: Restore missing Quantum reference definitions

2026-05-24T00:31:19Z

Restore missing Quantum reference definitions

← Older revision		Revision as of 00:31, 24 May 2026
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	:<math>H = \sum_k \left( \frac{p_k^2}{2m} + \frac{1}{2} m \omega_k^2 q_k^2 \right)</math>		:<math>H = \sum_k \left( \frac{p_k^2}{2m} + \frac{1}{2} m \omega_k^2 q_k^2 \right)</math>

	where each mode <math>k</math> has coordinate <math>q_k</math> and momentum <math>p_k</math>.<ref name="MIT804"/>		where each mode <math>k</math> has coordinate <math>q_k</math> and momentum <math>p_k</math>.<ref name="MIT804">https://ocw.mit.edu/courses/8-04-quantum-physics-i-spring-2016/</ref>

	This shows that a complex system can be reduced to a collection of independent harmonic oscillators.		This shows that a complex system can be reduced to a collection of independent harmonic oscillators.
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	:<math>H = \sum_k \hbar \omega_k \left(n_k + \frac{1}{2}\right)</math>		:<math>H = \sum_k \hbar \omega_k \left(n_k + \frac{1}{2}\right)</math>

	where <math>n_k = 0,1,2,\dots</math> counts the number of quanta in mode <math>k</math>.<ref name="TongQFT"/>		where <math>n_k = 0,1,2,\dots</math> counts the number of quanta in mode <math>k</math>.<ref name="TongQFT">https://www.damtp.cam.ac.uk/user/tong/qft.html</ref>

	Each mode can therefore absorb or emit discrete energy packets.		Each mode can therefore absorb or emit discrete energy packets.
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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}}

Maintenance script: Normalize quantum page header order

2026-05-22T11:32:06Z

Normalize quantum page header order

← Older revision		Revision as of 11:32, 22 May 2026
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	{{Quantum book backlink\|Wavefunctions and modes}}		{{Quantum book backlink\|Wavefunctions and modes}}
	{{Quantum article nav\|previous=Physics:Quantum Standing waves and modes\|previous label=Standing waves and modes\|next=Physics:Quantum Density of states\|next label=Density of states}}		{{Quantum article nav\|previous=Physics:Quantum Standing waves and modes\|previous label=Standing waves and modes\|next=Physics:Quantum Density of states\|next label=Density of states}}

	<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

2026-05-22T11:10:23Z

Clean Book label remnants and backlink spacing

← Older revision		Revision as of 11:10, 22 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Normal modes and field quantization}}		{{Short description\|Quantum Collection topic on Quantum Normal modes and field quantization}}

	{{Quantum book backlink\|Wavefunctions and modes}}		{{Quantum book backlink\|Wavefunctions and modes}}
	{{Quantum article nav\|previous=Physics:Quantum Standing waves and modes\|previous label=Standing waves and modes\|next=Physics:Quantum Density of states\|next label=Density of states}}		{{Quantum article nav\|previous=Physics:Quantum Standing waves and modes\|previous label=Standing waves and modes\|next=Physics:Quantum Density of states\|next label=Density of states}}

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

2026-05-22T11:02:35Z

Remove hidden BOM characters and direct Book label after Short description

← Older revision		Revision as of 11:02, 22 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Normal modes and field quantization}}~~Book I~~		{{Short description\|Quantum Collection topic on Quantum Normal modes and field quantization}}

	{{Quantum book backlink\|Wavefunctions and modes}}		{{Quantum book backlink\|Wavefunctions and modes}}

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

2026-05-22T10:47:38Z

Clean Short description prefix and add Book I label

← Older revision		Revision as of 10:47, 22 May 2026
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	~~~~{{Short description\|Quantum Collection topic on Quantum Normal modes and field quantization}}		{{Short description\|Quantum Collection topic on Quantum Normal modes and field quantization}}Book I

	{{Quantum book backlink\|Wavefunctions and modes}}		{{Quantum book backlink\|Wavefunctions and modes}}

Maintenance script: Apply Quantum previous-next navigation

2026-05-20T12:24:14Z

Apply Quantum previous-next navigation

← Older revision		Revision as of 12:24, 20 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Normal modes and field quantization}}		{{Short description\|Quantum Collection topic on Quantum Normal modes and field quantization}}

	{{Quantum book backlink\|Wavefunctions and modes}}		{{Quantum book backlink\|Wavefunctions and modes}}
			{{Quantum article nav\|previous=Physics:Quantum Standing waves and modes\|previous label=Standing waves and modes\|next=Physics:Quantum Density of states\|next label=Density of states}}

	<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

2026-05-20T09:03:37Z

Improve Book I intro quality

← Older revision		Revision as of 09:03, 20 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Normal modes and field quantization}}		{{Short description\|Quantum Collection topic on Quantum Normal modes and field quantization}}

	{{Quantum book backlink\|Wavefunctions and modes}}		{{Quantum book backlink\|Wavefunctions and modes}}
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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;">
	'''Normal modes and field quantization''' ~~is a Book I topic in the Quantum Collection. Quantum~~ normal modes and field quantization describe how a physical system with many degrees of freedom can be decomposed into independent modes, each behaving like a quantum harmonic oscillator. This idea forms the foundation of quantum field theory and explains how particles such as photons and phonons arise from quantized fields. Quantum normal modes and field quantization describe how a physical system with many degrees of freedom can be decomposed into independent modes, each behaving like a quantum harmonic oscillator. This idea forms the foundation of quantum field theory and explains how particles such as photons and phonons arise from quantized fields. In classical physics, many systems can be decomposed into independent oscillations called normal modes.		'''Normal modes and field quantization''' quantum normal modes and field quantization describe how a physical system with many degrees of freedom can be decomposed into independent modes, each behaving like a quantum harmonic oscillator. This idea forms the foundation of quantum field theory and explains how particles such as photons and phonons arise from quantized fields. Quantum normal modes and field quantization describe how a physical system with many degrees of freedom can be decomposed into independent modes, each behaving like a quantum harmonic oscillator. This idea forms the foundation of quantum field theory and explains how particles such as photons and phonons arise from quantized fields. In classical physics, many systems can be decomposed into independent oscillations called normal modes.
	</div>		</div>

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

2026-05-20T08:13:39Z

Clean Book I red links, intro, and image slots

← Older revision		Revision as of 08:13, 20 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Normal modes and field quantization}}		{{Short description\|Quantum Collection topic on Quantum Normal modes and field quantization}}

	{{Quantum book backlink\|Wavefunctions and modes}}		{{Quantum book backlink\|Wavefunctions and modes}}
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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;">
	'''~~Quantum normal~~ modes and field quantization''' describe how a physical system with many degrees of freedom can be decomposed into independent modes, each behaving like a quantum harmonic oscillator. This idea forms the foundation of quantum field theory and explains how particles such as photons and phonons arise from quantized fields.~~<ref name="MIT804">https://ocw~~.~~mit~~.~~edu/courses/8-04-quantum-~~physics~~-i-spring-2016/</ref><ref name="TongQFT">https://www.damtp.cam.ac.uk/user/tong/qft~~.~~html</ref>~~		'''Normal modes and field quantization''' is a Book I topic in the Quantum Collection. Quantum normal modes and field quantization describe how a physical system with many degrees of freedom can be decomposed into independent modes, each behaving like a quantum harmonic oscillator. This idea forms the foundation of quantum field theory and explains how particles such as photons and phonons arise from quantized fields. Quantum normal modes and field quantization describe how a physical system with many degrees of freedom can be decomposed into independent modes, each behaving like a quantum harmonic oscillator. This idea forms the foundation of quantum field theory and explains how particles such as photons and phonons arise from quantized fields. In classical physics, many systems can be decomposed into independent oscillations called normal modes.
	</div>		</div>

Maintenance script: Normalize Book I Quantum page structure

2026-05-19T22:49:08Z

Normalize Book I Quantum page structure

← Older revision		Revision as of 22:49, 19 May 2026
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	[[Category:Physics]]		[[Category:Physics]]

	{{Sourceattribution\|Quantum Normal modes and field quantization\|1}}		{{Sourceattribution\|Physics:Quantum Normal modes and field quantization\|1}}

Harold: Arrange page top as TOC lead image columns

2026-05-17T14:00:24Z

Arrange page top as TOC lead image columns

@@ Line 1: / Line 1: @@
 {{Quantum book backlink|Wavefunctions and modes}}
 '''Quantum normal modes and field quantization''' describe how a physical system with many degrees of freedom can be decomposed into independent modes, each behaving like a quantum harmonic oscillator. This idea forms the foundation of quantum field theory and explains how particles such as photons and phonons arise from quantized fields.<ref name="MIT804">https://ocw.mit.edu/courses/8-04-quantum-physics-i-spring-2016/</ref><ref name="TongQFT">https://www.damtp.cam.ac.uk/user/tong/qft.html</ref>
-[[File:Quantum_normal_modes_field_quantization.svg|thumb|400px|Normal modes of a system behave as independent harmonic oscillators, forming the basis for field quantization and the emergence of particles such as photons and phonons.]]
+</div>
 == Normal modes in classical systems ==