Physics:Quantum Distribution functions - Revision history

WikiHarold: Restore missing Quantum reference definitions

2026-05-24T00:31:05Z

Restore missing Quantum reference definitions

← Older revision		Revision as of 00:31, 24 May 2026
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	For bosons:		For bosons:

	<math>f(E) = \frac{1}{e^{\beta(E-\mu)} - 1}</math><ref name="TongQG"/>		<math>f(E) = \frac{1}{e^{\beta(E-\mu)} - 1}</math><ref name="TongQG">https://www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S3.html</ref>

	Bosons can accumulate in low-energy states, leading to Bose–Einstein condensation.<ref name="MITBose">https://ocw.mit.edu/courses/8-08-statistical-physics-ii-spring-2005/resources/the_bose_gas/</ref>		Bosons can accumulate in low-energy states, leading to Bose–Einstein condensation.<ref name="MITBose">https://ocw.mit.edu/courses/8-08-statistical-physics-ii-spring-2005/resources/the_bose_gas/</ref>
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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}}

Maintenance script: Normalize quantum page header order

2026-05-22T11:33:46Z

Normalize quantum page header order

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	{{Quantum book backlink\|Statistical mechanics and kinetic theory}}		{{Quantum book backlink\|Statistical mechanics and kinetic theory}}
	{{Quantum article nav\|previous=Physics:Quantum Partition function\|previous label=Partition function\|next=Physics:Quantum Liouville equation\|next label=Liouville equation}}		{{Quantum article nav\|previous=Physics:Quantum Partition function\|previous label=Partition function\|next=Physics:Quantum Liouville equation\|next label=Liouville equation}}

	<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

2026-05-22T11:12:04Z

Clean Book label remnants and backlink spacing

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	{{Short description\|Quantum Collection topic on Quantum Distribution functions}}		{{Short description\|Quantum Collection topic on Quantum Distribution functions}}

	{{Quantum book backlink\|Statistical mechanics and kinetic theory}}		{{Quantum book backlink\|Statistical mechanics and kinetic theory}}
	{{Quantum article nav\|previous=Physics:Quantum Partition function\|previous label=Partition function\|next=Physics:Quantum Liouville equation\|next label=Liouville equation}}		{{Quantum article nav\|previous=Physics:Quantum Partition function\|previous label=Partition function\|next=Physics:Quantum Liouville equation\|next label=Liouville equation}}

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

2026-05-22T11:04:17Z

Remove hidden BOM characters and direct Book label after Short description

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	{{Short description\|Quantum Collection topic on Quantum Distribution functions}}~~Book I~~		{{Short description\|Quantum Collection topic on Quantum Distribution functions}}

	{{Quantum book backlink\|Statistical mechanics and kinetic theory}}		{{Quantum book backlink\|Statistical mechanics and kinetic theory}}

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

2026-05-22T10:49:18Z

Clean Short description prefix and add Book I label

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	~~~~{{Short description\|Quantum Collection topic on Quantum Distribution functions}}		{{Short description\|Quantum Collection topic on Quantum Distribution functions}}Book I

	{{Quantum book backlink\|Statistical mechanics and kinetic theory}}		{{Quantum book backlink\|Statistical mechanics and kinetic theory}}

Maintenance script: Apply Quantum previous-next navigation

2026-05-20T12:26:31Z

Apply Quantum previous-next navigation

← Older revision		Revision as of 12:26, 20 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Distribution functions}}		{{Short description\|Quantum Collection topic on Quantum Distribution functions}}

	{{Quantum book backlink\|Statistical mechanics and kinetic theory}}		{{Quantum book backlink\|Statistical mechanics and kinetic theory}}
			{{Quantum article nav\|previous=Physics:Quantum Partition function\|previous label=Partition function\|next=Physics:Quantum Liouville equation\|next label=Liouville equation}}

	<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

2026-05-20T09:05:20Z

Improve Book I intro quality

← Older revision		Revision as of 09:05, 20 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Distribution functions}}		{{Short description\|Quantum Collection topic on Quantum Distribution functions}}

	{{Quantum book backlink\|Statistical mechanics and kinetic theory}}		{{Quantum book backlink\|Statistical mechanics and kinetic theory}}
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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;">
	'''Distribution functions''' ~~is a Book I topic in the Quantum Collection. Quantum~~ distribution functions describe the average occupation of energy states in a many-particle system at thermal equilibrium. They distinguish classical from quantum statistical behavior. For a state of energy E, the occupation depends on particle type. Quantum distribution functions describe the average occupation of energy states in a many-particle system at thermal equilibrium. They distinguish classical from quantum statistical behavior. For a state of energy E, the occupation depends on particle type. Bosons can accumulate in low-energy states, leading to Bose–Einstein condensation. The Pauli exclusion principle limits occupation to one particle per state. At low temperature, the distribution approaches a step function at the Fermi energy.		'''Distribution functions''' quantum distribution functions describe the average occupation of energy states in a many-particle system at thermal equilibrium. They distinguish classical from quantum statistical behavior. For a state of energy E, the occupation depends on particle type. Quantum distribution functions describe the average occupation of energy states in a many-particle system at thermal equilibrium. They distinguish classical from quantum statistical behavior. For a state of energy E, the occupation depends on particle type. Bosons can accumulate in low-energy states, leading to Bose–Einstein condensation. The Pauli exclusion principle limits occupation to one particle per state. At low temperature, the distribution approaches a step function at the Fermi energy.
	</div>		</div>

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

2026-05-20T08:17:02Z

Clean Book I red links, intro, and image slots

← Older revision		Revision as of 08:17, 20 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Distribution functions}}		{{Short description\|Quantum Collection topic on Quantum Distribution functions}}

	{{Quantum book backlink\|Statistical mechanics and kinetic theory}}		{{Quantum book backlink\|Statistical mechanics and kinetic theory}}
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	'''~~Quantum distribution~~ functions''' describe the average occupation of energy states in a many-particle system at thermal equilibrium. They distinguish classical from quantum statistical behavior.		'''Distribution functions''' is a Book I topic in the Quantum Collection. Quantum distribution functions describe the average occupation of energy states in a many-particle system at thermal equilibrium. They distinguish classical from quantum statistical behavior. For a state of energy E, the occupation depends on particle type. Quantum distribution functions describe the average occupation of energy states in a many-particle system at thermal equilibrium. They distinguish classical from quantum statistical behavior. For a state of energy E, the occupation depends on particle type. Bosons can accumulate in low-energy states, leading to Bose–Einstein condensation. The Pauli exclusion principle limits occupation to one particle per state. At low temperature, the distribution approaches a step function at the Fermi energy.

	For a state of energy ~~<math>~~E~~</math>~~, the occupation depends on particle type.~~<ref name="TongQG">https://www~~.~~damtp~~.~~cam~~.ac.~~uk/user/tong/statphys/statmechhtml/S3~~.~~html</ref>~~
	</div>		</div>

Maintenance script: Extend distribution functions context

2026-05-19T23:17:01Z

Extend distribution functions context

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	== Additional context ==		== Additional context ==
	Distribution functions also provide a bridge between microscopic quantum states and macroscopic observables. They are useful when individual amplitudes are less important than populations, occupation numbers, transition rates, or statistical averages over many states.		Distribution functions also provide a bridge between microscopic quantum states and macroscopic observables. They are useful when individual amplitudes are less important than populations, occupation numbers, transition rates, or statistical averages over many states.

			They also make it easier to compare equilibrium, near-equilibrium, and driven systems using a common statistical language.

	==See also==		==See also==

Maintenance script: Extend short Book I page text

2026-05-19T23:15:58Z

Extend short Book I page text

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	== Related measurements ==		== Related measurements ==
	Typical measurements involve spectra, decay products, transition rates, transport behavior, correlation functions, or detector signatures. These observations provide the empirical link between the page topic and the wider Quantum Collection.		Typical measurements involve spectra, decay products, transition rates, transport behavior, correlation functions, or detector signatures. These observations provide the empirical link between the page topic and the wider Quantum Collection.

			== Additional context ==
			Distribution functions also provide a bridge between microscopic quantum states and macroscopic observables. They are useful when individual amplitudes are less important than populations, occupation numbers, transition rates, or statistical averages over many states.

	==See also==		==See also==

← Older revision		Revision as of 11:12, 22 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Distribution functions}}		{{Short description\|Quantum Collection topic on Quantum Distribution functions}}

	{{Quantum book backlink\|Statistical mechanics and kinetic theory}}		{{Quantum book backlink\|Statistical mechanics and kinetic theory}}
	{{Quantum article nav\|previous=Physics:Quantum Partition function\|previous label=Partition function\|next=Physics:Quantum Liouville equation\|next label=Liouville equation}}		{{Quantum article nav\|previous=Physics:Quantum Partition function\|previous label=Partition function\|next=Physics:Quantum Liouville equation\|next label=Liouville equation}}