Physics:Quantum Approximation Methods - Revision history

WikiHarold: Restore missing Quantum reference definitions

2026-05-24T00:31:01Z

Restore missing Quantum reference definitions

← Older revision		Revision as of 00:31, 24 May 2026
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	== WKB Approximation ==		== WKB Approximation ==

	The Wentzel–Kramers–Brillouin (WKB) approximation is a semiclassical method applicable when the potential varies slowly compared to the particle’s wavelength.<ref name="cohen" />		The Wentzel–Kramers–Brillouin (WKB) approximation is a semiclassical method applicable when the potential varies slowly compared to the particle’s wavelength.<ref name="cohen">Cohen-Tannoudji, C., Diu, B., & Laloë, F. (1977). ''Quantum Mechanics''. Wiley.</ref>

	The approximate solution to the Schrödinger equation is:		The approximate solution to the Schrödinger equation is:
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	* Scattering theory		* Scattering theory

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

Maintenance script: Normalize quantum page header order

2026-05-22T11:31:42Z

Normalize quantum page header order

← Older revision		Revision as of 11:31, 22 May 2026
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	{{Quantum book backlink\|Mathematical structure and systems}}		{{Quantum book backlink\|Mathematical structure and systems}}
	{{Quantum article nav\|previous=Physics:Quantum Runge–Lenz vector\|previous label=Runge–Lenz vector\|next=Physics:Quantum Matter Elements and Particles\|next label=Matter Elements and Particles}}		{{Quantum article nav\|previous=Physics:Quantum Runge–Lenz vector\|previous label=Runge–Lenz vector\|next=Physics:Quantum Matter Elements and Particles\|next label=Matter Elements and Particles}}

	<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

2026-05-22T11:09:59Z

Clean Book label remnants and backlink spacing

← Older revision		Revision as of 11:09, 22 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}		{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}

	{{Quantum book backlink\|Mathematical structure and systems}}		{{Quantum book backlink\|Mathematical structure and systems}}
	{{Quantum article nav\|previous=Physics:Quantum Runge–Lenz vector\|previous label=Runge–Lenz vector\|next=Physics:Quantum Matter Elements and Particles\|next label=Matter Elements and Particles}}		{{Quantum article nav\|previous=Physics:Quantum Runge–Lenz vector\|previous label=Runge–Lenz vector\|next=Physics:Quantum Matter Elements and Particles\|next label=Matter Elements and Particles}}

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

2026-05-22T11:02:12Z

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 Approximation Methods}}~~Book I~~		{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}

	{{Quantum book backlink\|Mathematical structure and systems}}		{{Quantum book backlink\|Mathematical structure and systems}}

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

2026-05-22T10:47:13Z

Clean Short description prefix and add Book I label

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	~~~~{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}		{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}Book I

	{{Quantum book backlink\|Mathematical structure and systems}}		{{Quantum book backlink\|Mathematical structure and systems}}

Maintenance script: Apply Quantum previous-next navigation

2026-05-20T12:23:32Z

Apply Quantum previous-next navigation

← Older revision		Revision as of 12:23, 20 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}		{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}

	{{Quantum book backlink\|Mathematical structure and systems}}		{{Quantum book backlink\|Mathematical structure and systems}}
			{{Quantum article nav\|previous=Physics:Quantum Runge–Lenz vector\|previous label=Runge–Lenz vector\|next=Physics:Quantum Matter Elements and Particles\|next label=Matter Elements and Particles}}

	<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

2026-05-20T09:03:05Z

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 Approximation Methods}}		{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}

	{{Quantum book backlink\|Mathematical structure and systems}}		{{Quantum book backlink\|Mathematical structure and systems}}
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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;">
	'''Approximation Methods''' ~~is a Book I topic~~ in ~~the Quantum Collection. In~~ most physical systems, the Hamiltonian contains interactions that make exact solutions intractable. Approximation methods provide systematic procedures to estimate eigenvalues, eigenfunctions, and dynamical behavior with accuracy. These methods are used in atomic physics, molecular physics, condensed matter physics, and quantum field theory. In most physical systems, the Hamiltonian contains interactions that make exact solutions intractable. Approximation methods provide systematic procedures to estimate eigenvalues, eigenfunctions, and dynamical behavior with accuracy. These methods are used in atomic physics, molecular physics, condensed matter physics, and quantum field theory. Quantum approximation methods are a group of analytical and semi-analytical techniques used to find approximate solutions to quantum mechanical problems that cannot be solved exactly.		'''Approximation Methods''' in most physical systems, the Hamiltonian contains interactions that make exact solutions intractable. Approximation methods provide systematic procedures to estimate eigenvalues, eigenfunctions, and dynamical behavior with accuracy. These methods are used in atomic physics, molecular physics, condensed matter physics, and quantum field theory. In most physical systems, the Hamiltonian contains interactions that make exact solutions intractable. Approximation methods provide systematic procedures to estimate eigenvalues, eigenfunctions, and dynamical behavior with accuracy. These methods are used in atomic physics, molecular physics, condensed matter physics, and quantum field theory. Quantum approximation methods are a group of analytical and semi-analytical techniques used to find approximate solutions to quantum mechanical problems that cannot be solved exactly.
	</div>		</div>

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

2026-05-20T08:12:45Z

Clean Book I red links, intro, and image slots

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	{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}		{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}

	{{Quantum book backlink\|Mathematical structure and systems}}		{{Quantum book backlink\|Mathematical structure and systems}}
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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;">
	In most physical systems, the Hamiltonian contains interactions that make exact solutions intractable. Approximation methods provide systematic procedures to estimate eigenvalues, eigenfunctions, and dynamical behavior with accuracy. These methods are used in atomic physics, molecular physics, condensed matter physics, and quantum field theory.~~<ref name="cohen">Cohen-Tannoudji~~, C., ~~Diu~~, B., ~~& Laloë~~, F. ~~(1977). ''~~Quantum ~~Mechanics''. Wiley~~.~~</ref>~~		'''Approximation Methods''' is a Book I topic in the Quantum Collection. In most physical systems, the Hamiltonian contains interactions that make exact solutions intractable. Approximation methods provide systematic procedures to estimate eigenvalues, eigenfunctions, and dynamical behavior with accuracy. These methods are used in atomic physics, molecular physics, condensed matter physics, and quantum field theory. In most physical systems, the Hamiltonian contains interactions that make exact solutions intractable. Approximation methods provide systematic procedures to estimate eigenvalues, eigenfunctions, and dynamical behavior with accuracy. These methods are used in atomic physics, molecular physics, condensed matter physics, and quantum field theory. Quantum approximation methods are a group of analytical and semi-analytical techniques used to find approximate solutions to quantum mechanical problems that cannot be solved exactly.
	</div>		</div>

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	==See also==		==See also==
	{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}
	* [[Schrödinger equation]]		* Schrödinger equation
	* [[Perturbation theory (quantum mechanics)]]		* Perturbation theory (quantum mechanics)
	* [[Scattering theory]]		* Scattering theory

	== References ==		== References ==

Maintenance script: Normalize Book I Quantum page structure

2026-05-19T22:48:44Z

Normalize Book I Quantum page structure

← Older revision		Revision as of 22:48, 19 May 2026
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	[[Category:Physics]]		[[Category:Physics]]

	{{Sourceattribution\|Quantum Approximation Methods\|1}}		{{Sourceattribution\|Physics:Quantum Approximation Methods\|1}}

Harold: Clean Quantum header BOM and legacy backlink

2026-05-17T22:04:46Z

Clean Quantum header BOM and legacy backlink

← Older revision		Revision as of 22:04, 17 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}		{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}

	{{Quantum book backlink\|Mathematical structure and systems}}		{{Quantum book backlink\|Mathematical structure and systems}}

← Older revision		Revision as of 11:09, 22 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}		{{Short description\|Quantum Collection topic on Quantum Approximation Methods}}

	{{Quantum book backlink\|Mathematical structure and systems}}		{{Quantum book backlink\|Mathematical structure and systems}}
	{{Quantum article nav\|previous=Physics:Quantum Runge–Lenz vector\|previous label=Runge–Lenz vector\|next=Physics:Quantum Matter Elements and Particles\|next label=Matter Elements and Particles}}		{{Quantum article nav\|previous=Physics:Quantum Runge–Lenz vector\|previous label=Runge–Lenz vector\|next=Physics:Quantum Matter Elements and Particles\|next label=Matter Elements and Particles}}