Physics:Quantum Scattering matrix - Revision history

WikiHarold: Expand short Quantum intro

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	\|image=[[File:Quantum_scattering_matrix_yellow.png\|430px\|Scattering matrix connecting incoming and outgoing quantum states.]]		\|image=[[File:Quantum_scattering_matrix_yellow.png\|430px\|Scattering matrix connecting incoming and outgoing quantum states.]]
	\|text=The ~~'''Quantum~~ scattering matrix~~''', or '''~~S-matrix~~''', is a mathematical object that~~ relates incoming quantum states before an interaction to outgoing states after the interaction. It is ~~widely used~~ in ~~scattering theory,~~ particle physics, nuclear physics, and ~~quantum field~~ theory.~~<ref>{{cite web \|url=https://en.wikipedia.org/wiki/S-matrix \|title=S-matrix \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>~~		\|text=The scattering matrix is a Book I topic in the Quantum Collection. The S-matrix relates incoming quantum states before an interaction to outgoing states after the interaction, avoiding the need to describe every detail of the intermediate process. Its elements encode transition amplitudes, cross sections, resonances, phase shifts, and conservation laws. The concept is central in particle physics, quantum field theory, nuclear physics, and scattering theory. It connects experimental observables with the abstract structure of unitary time evolution.

	~~ScholarlyWiki also has~~ the related page [[Physics:Quantum S-matrix\|Quantum S-matrix]]. This page gives the broader conceptual entry point, while the S-matrix page can hold more formal details, examples, and field-theory notation.
	}}		}}
	== Incoming and outgoing states ==		== Incoming and outgoing states ==

WikiHarold: Use Quantum See also index module

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	== See also ==		== See also ==
	* [[Physics:Quantum Scattering theory]]		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}
	* [[Physics:Quantum S-matrix]]
	* [[Physics:~~Quantum Feynman diagrams]]~~
	* [[Physics:Quantum ~~Path integral formulation]]~~

	== References ==		== References ==

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	{{Short description\|Matrix connecting incoming and outgoing quantum scattering states}}		{{Short description\|Matrix connecting incoming and outgoing quantum scattering states}}
			{{Quantum book backlink\|Quantum dynamics and evolution}}
			{{Quantum article nav\|previous=Physics:Quantum Scattering theory\|previous label=Scattering theory\|next=Physics:Quantum S-matrix\|next label=S-matrix}}
	{{ScholarlyWiki page top		{{ScholarlyWiki page top
	\|backlink=~~{{Quantum book backlink\|Quantum dynamics and evolution}}~~		\|backlink=
	~~{{Quantum article nav\|previous=Physics:Quantum Scattering theory\|previous label=Scattering theory\|next=Physics:Quantum S-matrix\|next label=S-matrix}}~~
	\|image=[[File:Quantum_scattering_matrix_yellow.png\|430px\|Scattering matrix connecting incoming and outgoing quantum states.]]		\|image=[[File:Quantum_scattering_matrix_yellow.png\|430px\|Scattering matrix connecting incoming and outgoing quantum states.]]
	\|text=The '''Quantum scattering matrix''', or '''S-matrix''', is a mathematical object that relates incoming quantum states before an interaction to outgoing states after the interaction. It is widely used in scattering theory, particle physics, nuclear physics, and quantum field theory.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/S-matrix \|title=S-matrix \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>		\|text=The '''Quantum scattering matrix''', or '''S-matrix''', is a mathematical object that relates incoming quantum states before an interaction to outgoing states after the interaction. It is widely used in scattering theory, particle physics, nuclear physics, and quantum field theory.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/S-matrix \|title=S-matrix \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>
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	ScholarlyWiki also has the related page [[Physics:Quantum S-matrix\|Quantum S-matrix]]. This page gives the broader conceptual entry point, while the S-matrix page can hold more formal details, examples, and field-theory notation.		ScholarlyWiki also has the related page [[Physics:Quantum S-matrix\|Quantum S-matrix]]. This page gives the broader conceptual entry point, while the S-matrix page can hold more formal details, examples, and field-theory notation.
	}}		}}

	== Incoming and outgoing states ==		== Incoming and outgoing states ==
	In scattering problems, particles or waves begin in a prepared incoming state, interact in a finite region, and are later detected in outgoing channels. The scattering matrix encodes the amplitudes for each allowed transition.		In scattering problems, particles or waves begin in a prepared incoming state, interact in a finite region, and are later detected in outgoing channels. The scattering matrix encodes the amplitudes for each allowed transition.

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2026-05-22T11:19:00Z

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	{{Short description\|Matrix connecting incoming and outgoing quantum scattering states}}		{{Short description\|Matrix connecting incoming and outgoing quantum scattering states}}

	{{ScholarlyWiki page top		{{ScholarlyWiki page top
	\|backlink={{Quantum book backlink\|Quantum dynamics and evolution}}		\|backlink={{Quantum book backlink\|Quantum dynamics and evolution}}

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	{{Short description\|Matrix connecting incoming and outgoing quantum scattering states}}~~Book I~~		{{Short description\|Matrix connecting incoming and outgoing quantum scattering states}}

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	{{Quantum article nav\|previous=Physics:Quantum Scattering theory\|previous label=Scattering theory\|next=Physics:Quantum S-matrix\|next label=S-matrix}}		{{Quantum article nav\|previous=Physics:Quantum Scattering theory\|previous label=Scattering theory\|next=Physics:Quantum S-matrix\|next label=S-matrix}}
			\|image=[[File:Quantum_scattering_matrix_yellow.png\|430px\|Scattering matrix connecting incoming and outgoing quantum states.]]
	[[File:Quantum_scattering_matrix_yellow.png\|~~thumb\|right\|320px~~\|Scattering matrix connecting incoming and outgoing quantum states.]]		\|text=The '''Quantum scattering matrix''', or '''S-matrix''', is a mathematical object that relates incoming quantum states before an interaction to outgoing states after the interaction. It is widely used in scattering theory, particle physics, nuclear physics, and quantum field theory.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/S-matrix \|title=S-matrix \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	The '''Quantum scattering matrix''', or '''S-matrix''', is a mathematical object that relates incoming quantum states before an interaction to outgoing states after the interaction. It is widely used in scattering theory, particle physics, nuclear physics, and quantum field theory.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/S-matrix \|title=S-matrix \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	ScholarlyWiki also has the related page [[Physics:Quantum S-matrix\|Quantum S-matrix]]. This page gives the broader conceptual entry point, while the S-matrix page can hold more formal details, examples, and field-theory notation.		ScholarlyWiki also has the related page [[Physics:Quantum S-matrix\|Quantum S-matrix]]. This page gives the broader conceptual entry point, while the S-matrix page can hold more formal details, examples, and field-theory notation.
			}}

	== Incoming and outgoing states ==		== Incoming and outgoing states ==

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	{{Quantum article nav\|previous=Physics:Quantum Scattering theory\|previous label=Scattering theory\|next=Physics:Quantum S-matrix\|next label=S-matrix}}		{{Quantum article nav\|previous=Physics:Quantum Scattering theory\|previous label=Scattering theory\|next=Physics:Quantum S-matrix\|next label=S-matrix}}

	~~<div style="display~~:~~flex; gap:24px; align-items:flex-start; max-width:1280px; clear:both;">~~		[[File:Quantum_scattering_matrix_yellow.png\|thumb\|right\|320px\|Scattering matrix connecting incoming and outgoing quantum states.]]
	~~<div style="flex:1 1 680px; min-width:0; line-height:1.55;">~~
	The '''Quantum scattering matrix''', or '''S-matrix''', is a mathematical object that relates incoming quantum states before an interaction to outgoing states after the interaction. It is widely used in scattering theory, particle physics, nuclear physics, and quantum field theory.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/S-matrix \|title=S-matrix \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>		The '''Quantum scattering matrix''', or '''S-matrix''', is a mathematical object that relates incoming quantum states before an interaction to outgoing states after the interaction. It is widely used in scattering theory, particle physics, nuclear physics, and quantum field theory.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/S-matrix \|title=S-matrix \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	ScholarlyWiki also has the related page [[Physics:Quantum S-matrix\|Quantum S-matrix]]. This page gives the broader conceptual entry point, while the S-matrix page can hold more formal details, examples, and field-theory notation.		ScholarlyWiki also has the related page [[Physics:Quantum S-matrix\|Quantum S-matrix]]. This page gives the broader conceptual entry point, while the S-matrix page can hold more formal details, examples, and field-theory notation.
	~~</div>~~
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	~~[[File:Quantum_scattering_matrix_yellow.png\|thumb\|360px\|Scattering matrix connecting incoming and outgoing quantum states.]]~~
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	== Incoming and outgoing states ==		== Incoming and outgoing states ==

Maintenance script: Improve top layout for Quantum concept page

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	{{Quantum article nav\|previous=Physics:Quantum Scattering theory\|previous label=Scattering theory\|next=Physics:Quantum S-matrix\|next label=S-matrix}}		{{Quantum article nav\|previous=Physics:Quantum Scattering theory\|previous label=Scattering theory\|next=Physics:Quantum S-matrix\|next label=S-matrix}}

	~~[[File~~:~~Quantum_scattering_matrix_yellow~~.~~png\|thumb\|280px\|Scattering matrix connecting incoming and outgoing quantum states.]]~~		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1280px; clear:both;">
			<div style="flex:1 1 680px; min-width:0; line-height:1.55;">
	The '''Quantum scattering matrix''', or '''S-matrix''', is a mathematical object that relates incoming quantum states before an interaction to outgoing states after the interaction. It is widely used in scattering theory, particle physics, nuclear physics, and quantum field theory.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/S-matrix \|title=S-matrix \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>		The '''Quantum scattering matrix''', or '''S-matrix''', is a mathematical object that relates incoming quantum states before an interaction to outgoing states after the interaction. It is widely used in scattering theory, particle physics, nuclear physics, and quantum field theory.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/S-matrix \|title=S-matrix \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	ScholarlyWiki also has the related page [[Physics:Quantum S-matrix\|Quantum S-matrix]]. This page gives the broader conceptual entry point, while the S-matrix page can hold more formal details, examples, and field-theory notation.		ScholarlyWiki also has the related page [[Physics:Quantum S-matrix\|Quantum S-matrix]]. This page gives the broader conceptual entry point, while the S-matrix page can hold more formal details, examples, and field-theory notation.
			</div>
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			[[File:Quantum_scattering_matrix_yellow.png\|thumb\|360px\|Scattering matrix connecting incoming and outgoing quantum states.]]
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			<div style="clear:both;"></div>

	== Incoming and outgoing states ==		== Incoming and outgoing states ==

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	[[File:Quantum_scattering_matrix_yellow.png\|thumb\|280px\|Scattering matrix connecting incoming and outgoing quantum states.]]		[[File:Quantum_scattering_matrix_yellow.png\|thumb\|280px\|Scattering matrix connecting incoming and outgoing quantum states.]]

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	{{Quantum article nav\|previous=Physics:Quantum Scattering theory\|previous label=Scattering theory\|next=Physics:Quantum S-matrix\|next label=S-matrix}}		{{Quantum article nav\|previous=Physics:Quantum Scattering theory\|previous label=Scattering theory\|next=Physics:Quantum S-matrix\|next label=S-matrix}}
			\|image=[[File:Quantum_scattering_matrix_yellow.png\|430px\|Scattering matrix connecting incoming and outgoing quantum states.]]
	[[File:Quantum_scattering_matrix_yellow.png\|~~thumb\|right\|320px~~\|Scattering matrix connecting incoming and outgoing quantum states.]]		\|text=The '''Quantum scattering matrix''', or '''S-matrix''', is a mathematical object that relates incoming quantum states before an interaction to outgoing states after the interaction. It is widely used in scattering theory, particle physics, nuclear physics, and quantum field theory.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/S-matrix \|title=S-matrix \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	The '''Quantum scattering matrix''', or '''S-matrix''', is a mathematical object that relates incoming quantum states before an interaction to outgoing states after the interaction. It is widely used in scattering theory, particle physics, nuclear physics, and quantum field theory.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/S-matrix \|title=S-matrix \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	ScholarlyWiki also has the related page [[Physics:Quantum S-matrix\|Quantum S-matrix]]. This page gives the broader conceptual entry point, while the S-matrix page can hold more formal details, examples, and field-theory notation.		ScholarlyWiki also has the related page [[Physics:Quantum S-matrix\|Quantum S-matrix]]. This page gives the broader conceptual entry point, while the S-matrix page can hold more formal details, examples, and field-theory notation.
			}}

	== Incoming and outgoing states ==		== Incoming and outgoing states ==

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			{{Quantum article nav\|previous=Physics:Quantum Scattering theory\|previous label=Scattering theory\|next=Physics:Quantum S-matrix\|next label=S-matrix}}

	[[File:Quantum_scattering_matrix_yellow.png\|thumb\|280px\|Scattering matrix connecting incoming and outgoing quantum states.]]		[[File:Quantum_scattering_matrix_yellow.png\|thumb\|280px\|Scattering matrix connecting incoming and outgoing quantum states.]]