Physics:Quantum Fermi's golden rule - Revision history

WikiHarold: Fix missing named reference on Fermi's golden rule

2026-05-24T00:14:04Z

Fix missing named reference on Fermi's golden rule

← Older revision		Revision as of 00:14, 24 May 2026
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	== Basic idea ==		== Basic idea ==

	If a Hamiltonian is written as <math>H = H_0 + V</math>, where <math>H_0</math> is the unperturbed Hamiltonian and <math>V</math> is a weak interaction, then the perturbation can induce transitions from an initial eigenstate <math>\|i\rangle</math> of <math>H_0</math> to final states <math>\|f\rangle</math>. In the long-time limit, and for weak coupling, the transition rate is proportional to the square of the matrix element <math>\langle f\|V\|i\rangle</math> and to the density of final states at the allowed energy.<ref name="LibreTextsChong"/><ref name="MIT806">[https://ocw.mit.edu/courses/8-06-quantum-physics-iii-spring-2018/89ef6d5958ee59bae9a91345c3d8c8e4_MIT8_06S18ch4.pdf Quantum Physics III, Chapter 4: Time Dependent Perturbation Theory, MIT OpenCourseWare]</ref>		If a Hamiltonian is written as <math>H = H_0 + V</math>, where <math>H_0</math> is the unperturbed Hamiltonian and <math>V</math> is a weak interaction, then the perturbation can induce transitions from an initial eigenstate <math>\|i\rangle</math> of <math>H_0</math> to final states <math>\|f\rangle</math>. In the long-time limit, and for weak coupling, the transition rate is proportional to the square of the matrix element <math>\langle f\|V\|i\rangle</math> and to the density of final states at the allowed energy.<ref name="LibreTextsChong">[https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_%28Chong%29/02%3A_Resonances/2.04%3A_Fermi%27s_Golden_Rule 2.4: Fermi's Golden Rule, Physics LibreTexts]</ref><ref name="MIT806">[https://ocw.mit.edu/courses/8-06-quantum-physics-iii-spring-2018/89ef6d5958ee59bae9a91345c3d8c8e4_MIT8_06S18ch4.pdf Quantum Physics III, Chapter 4: Time Dependent Perturbation Theory, MIT OpenCourseWare]</ref>

	== Standard formula ==		== Standard formula ==
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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 Fermi's golden rule\|1}}		{{Sourceattribution\|Physics:Quantum Fermi's golden rule\|1}}

Maintenance script: Normalize quantum page header order

2026-05-22T11:32:00Z

Normalize quantum page header order

← Older revision		Revision as of 11:32, 22 May 2026
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	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}
	{{Quantum article nav\|previous=Physics:Quantum Selection rules\|previous label=Selection rules\|next=Physics:Quantum beats\|next label=Beats}}		{{Quantum article nav\|previous=Physics:Quantum Selection rules\|previous label=Selection rules\|next=Physics:Quantum beats\|next label=Beats}}

	<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

2026-05-22T11:10:18Z

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 Fermi's golden rule}}		{{Short description\|Quantum Collection topic on Quantum Fermi's golden rule}}

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}
	{{Quantum article nav\|previous=Physics:Quantum Selection rules\|previous label=Selection rules\|next=Physics:Quantum beats\|next label=Beats}}		{{Quantum article nav\|previous=Physics:Quantum Selection rules\|previous label=Selection rules\|next=Physics:Quantum beats\|next label=Beats}}

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

2026-05-22T11:02:29Z

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 Fermi's golden rule}}~~Book I~~		{{Short description\|Quantum Collection topic on Quantum Fermi's golden rule}}

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}

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

2026-05-22T10:47:32Z

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 Fermi's golden rule}}		{{Short description\|Quantum Collection topic on Quantum Fermi's golden rule}}Book I

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}

Maintenance script: Apply Quantum previous-next navigation

2026-05-20T12:24:03Z

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 Fermi's golden rule}}		{{Short description\|Quantum Collection topic on Quantum Fermi's golden rule}}

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}
			{{Quantum article nav\|previous=Physics:Quantum Selection rules\|previous label=Selection rules\|next=Physics:Quantum beats\|next label=Beats}}

	<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

2026-05-20T09:03:27Z

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 Fermi's golden rule}}		{{Short description\|Quantum Collection topic on Quantum Fermi's golden rule}}

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}
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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;">
	'''Fermi's golden rule''' ~~is a Book I topic in the Quantum Collection. Quantum~~ Fermi's golden rule describes the transition rate from an initial quantum state to a set of final states when a weak perturbation acts on the system. It is one of the standard results of time-dependent perturbation theory and is especially important when the final states form a continuum, such as in atomic decay, ionization, scattering, and optical absorption. Quantum Fermi's golden rule describes the transition rate from an initial quantum state to a set of final states when a weak perturbation acts on the system. It is one of the standard results of time-dependent perturbation theory and is especially important when the final states form a continuum, such as in atomic decay, ionization, scattering, and optical absorption.		'''Fermi's golden rule''' quantum Fermi's golden rule describes the transition rate from an initial quantum state to a set of final states when a weak perturbation acts on the system. It is one of the standard results of time-dependent perturbation theory and is especially important when the final states form a continuum, such as in atomic decay, ionization, scattering, and optical absorption. Quantum Fermi's golden rule describes the transition rate from an initial quantum state to a set of final states when a weak perturbation acts on the system. It is one of the standard results of time-dependent perturbation theory and is especially important when the final states form a continuum, such as in atomic decay, ionization, scattering, and optical absorption. For transitions into a continuum of final states, the usual form is
	</div>		</div>

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

2026-05-20T08:13:26Z

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 Fermi's golden rule}}		{{Short description\|Quantum Collection topic on Quantum Fermi's golden rule}}

	{{Quantum book backlink\|Atomic and spectroscopy}}		{{Quantum book backlink\|Atomic and spectroscopy}}
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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~~ Fermi's golden rule''' describes the transition rate from an initial quantum state to a set of final states when a weak perturbation acts on the system. It is one of the standard results of time-dependent perturbation theory and is especially important when the final states form a continuum, such as in atomic decay, ionization, scattering, and optical absorption.~~<ref name="LibreTextsChong">[https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_%28Chong%29/02%3A_Resonances/2.04%3A_Fermi%27s_Golden_Rule 2.4:~~ Fermi's ~~Golden Rule, Physics LibreTexts]</ref><ref name="LibreTextsTuckerman">[https://chem~~.~~libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Advanced_Statistical_Mechanics_%28Tuckerman%29/13%3A_Time~~-~~dependent_Processes_-_Quantum_Case/13~~.~~04%3A_Fermi%27s_Golden_Rule 13.4: Fermi's Golden Rule, Chemistry LibreTexts]</ref>~~		'''Fermi's golden rule''' is a Book I topic in the Quantum Collection. Quantum Fermi's golden rule describes the transition rate from an initial quantum state to a set of final states when a weak perturbation acts on the system. It is one of the standard results of time-dependent perturbation theory and is especially important when the final states form a continuum, such as in atomic decay, ionization, scattering, and optical absorption. Quantum Fermi's golden rule describes the transition rate from an initial quantum state to a set of final states when a weak perturbation acts on the system. It is one of the standard results of time-dependent perturbation theory and is especially important when the final states form a continuum, such as in atomic decay, ionization, scattering, and optical absorption.
	</div>		</div>

Maintenance script: Normalize Book I Quantum page structure

2026-05-19T22:49:01Z

Normalize Book I Quantum page structure

← Older revision		Revision as of 22:49, 19 May 2026
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	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

	{{Sourceattribution\|Quantum ~~Spectral lines and series~~\|1}}		{{Sourceattribution\|Physics:Quantum Fermi's golden rule\|1}}

Harold: Arrange page top as TOC lead image columns

2026-05-17T14:00:18Z

Arrange page top as TOC lead image columns

@@ Line 1: / Line 1: @@
 {{Quantum book backlink|Atomic and spectroscopy}}
 '''Quantum Fermi's golden rule''' describes the transition rate from an initial quantum state to a set of final states when a weak perturbation acts on the system. It is one of the standard results of time-dependent perturbation theory and is especially important when the final states form a continuum, such as in atomic decay, ionization, scattering, and optical absorption.<ref name="LibreTextsChong">[https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_%28Chong%29/02%3A_Resonances/2.04%3A_Fermi%27s_Golden_Rule 2.4: Fermi's Golden Rule, Physics LibreTexts]</ref><ref name="LibreTextsTuckerman">[https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Advanced_Statistical_Mechanics_%28Tuckerman%29/13%3A_Time-dependent_Processes_-_Quantum_Case/13.04%3A_Fermi%27s_Golden_Rule 13.4: Fermi's Golden Rule, Chemistry LibreTexts]</ref>
-[[File:Quantum_Fermis_golden_rule.svg|thumb|400px|Fermi's golden rule relates quantum transition rates to the coupling strength between states and the density of available final states.]]
+</div>
 == Basic idea ==