Physics:Quantum Scattering matrix - Revision history

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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}}
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	[[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.
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	== 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.]]
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	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.
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	== Incoming and outgoing states ==		== Incoming and outgoing states ==

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

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	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.
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	== 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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Create Quantum Collection concept page

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{{Short description|Matrix connecting incoming and outgoing quantum scattering states}}
{{Quantum book backlink|Quantum dynamics and evolution}}

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

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.

== 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.

Probabilities are obtained from the squared magnitudes of these amplitudes, while phases encode interference and resonance information.

== Role in quantum theory ==
The scattering matrix is important because many experiments observe particles long before and long after an interaction, not during the interaction itself. Collider events, atomic collisions, and wave scattering can all be organized in this language.

In quantum field theory, the S-matrix is constrained by unitarity, symmetry, causality, and conservation laws. It connects naturally with [[Physics:Quantum Feynman diagrams|Feynman diagrams]] and perturbation theory.

== See also ==
* [[Physics:Quantum Scattering theory]]
* [[Physics:Quantum S-matrix]]
* [[Physics:Quantum Feynman diagrams]]
* [[Physics:Quantum Path integral formulation]]

== References ==
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum Scattering matrix|1}}