Physics:Quantum many-body problem - Revision history

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	\|image=[[File:Quantum_many_body_problem_yellow.png\|430px\|Many interacting particles generate a rapidly growing quantum state space.]]		\|image=[[File:Quantum_many_body_problem_yellow.png\|430px\|Many interacting particles generate a rapidly growing quantum state space.]]
	\|text=The ~~'''~~quantum many-body problem~~'''~~ is the challenge of describing systems ~~containing~~ many interacting quantum particles~~. Because~~ the ~~state~~ space grows ~~extremely~~ rapidly with particle number~~, exact~~ solutions are ~~usually impossible except for small or specially structured systems~~.~~<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Many-body_problem \|title=Many-body~~ problem ~~\|publisher=Wikipedia \|access-date=20 May 2026}}</ref>~~		\|text=The quantum many-body problem is a Book I topic in the Quantum Collection. It is the challenge of describing systems made of many interacting quantum particles, where the size of the Hilbert space grows rapidly with particle number. Exact solutions are rare, so the field uses approximations, effective theories, numerical methods, and emergent collective descriptions. The problem appears in atoms, nuclei, solids, quantum fluids, plasmas, and quantum information. It explains why simple microscopic rules can produce phases, quasiparticles, correlations, and complex macroscopic behavior.

	~~Many-body physics~~ appears in atoms~~, molecules~~, nuclei, solids, quantum fluids, plasmas, and quantum information ~~systems~~. It ~~connects~~ microscopic ~~quantum laws with collective behavior such as magnetism~~, ~~superconductivity~~, ~~phase transitions~~, and ~~emergent quasiparticles~~.
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	== State-space growth ==		== State-space growth ==

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	== See also ==		== See also ==
	* [[Physics:Quantum Approximation Methods]]		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}
	* [[Physics:Quantum Statistical mechanics]]
	* [[Physics:~~Quantum Fock space]]~~
	* [[Physics:Quantum ~~Exchange interaction]]~~

	== References ==		== References ==

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	{{Short description\|Problem of describing interacting systems with many quantum particles}}		{{Short description\|Problem of describing interacting systems with many quantum particles}}
			{{Quantum book backlink\|Mathematical structure and systems}}
			{{Quantum article nav\|previous=Physics:Quantum Exactly solvable quantum systems\|previous label=Exactly solvable quantum systems\|next=Physics:Quantum Formulas Collection\|next label=Formulas Collection}}
	{{ScholarlyWiki page top		{{ScholarlyWiki page top
	\|backlink=~~{{Quantum book backlink\|Mathematical structure and systems}}~~		\|backlink=
	{{Quantum article nav\|previous=Physics:Quantum Exactly solvable quantum systems\|previous label=Exactly solvable quantum systems\|next=Physics:Quantum Formulas Collection\|next label=Formulas Collection}}
	\|image=[[File:Quantum_many_body_problem_yellow.png\|430px\|Many interacting particles generate a rapidly growing quantum state space.]]		\|image=[[File:Quantum_many_body_problem_yellow.png\|430px\|Many interacting particles generate a rapidly growing quantum state space.]]
	\|text=The '''quantum many-body problem''' is the challenge of describing systems containing many interacting quantum particles. Because the state space grows extremely rapidly with particle number, exact solutions are usually impossible except for small or specially structured systems.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Many-body_problem \|title=Many-body problem \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>		\|text=The '''quantum many-body problem''' is the challenge of describing systems containing many interacting quantum particles. Because the state space grows extremely rapidly with particle number, exact solutions are usually impossible except for small or specially structured systems.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Many-body_problem \|title=Many-body problem \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>
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	Many-body physics appears in atoms, molecules, nuclei, solids, quantum fluids, plasmas, and quantum information systems. It connects microscopic quantum laws with collective behavior such as magnetism, superconductivity, phase transitions, and emergent quasiparticles.		Many-body physics appears in atoms, molecules, nuclei, solids, quantum fluids, plasmas, and quantum information systems. It connects microscopic quantum laws with collective behavior such as magnetism, superconductivity, phase transitions, and emergent quasiparticles.
	}}		}}

	== State-space growth ==		== State-space growth ==
	For a single particle, a wavefunction may be described over ordinary space. For many particles, the wavefunction depends on all particle coordinates and internal degrees of freedom. The number of amplitudes needed to represent the state can grow exponentially.		For a single particle, a wavefunction may be described over ordinary space. For many particles, the wavefunction depends on all particle coordinates and internal degrees of freedom. The number of amplitudes needed to represent the state can grow exponentially.

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			\|image=[[File:Quantum_many_body_problem_yellow.png\|430px\|Many interacting particles generate a rapidly growing quantum state space.]]
	[[File:Quantum_many_body_problem_yellow.png\|~~thumb\|right\|320px~~\|Many interacting particles generate a rapidly growing quantum state space.]]		\|text=The '''quantum many-body problem''' is the challenge of describing systems containing many interacting quantum particles. Because the state space grows extremely rapidly with particle number, exact solutions are usually impossible except for small or specially structured systems.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Many-body_problem \|title=Many-body problem \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	The '''quantum many-body problem''' is the challenge of describing systems containing many interacting quantum particles. Because the state space grows extremely rapidly with particle number, exact solutions are usually impossible except for small or specially structured systems.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Many-body_problem \|title=Many-body problem \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	Many-body physics appears in atoms, molecules, nuclei, solids, quantum fluids, plasmas, and quantum information systems. It connects microscopic quantum laws with collective behavior such as magnetism, superconductivity, phase transitions, and emergent quasiparticles.		Many-body physics appears in atoms, molecules, nuclei, solids, quantum fluids, plasmas, and quantum information systems. It connects microscopic quantum laws with collective behavior such as magnetism, superconductivity, phase transitions, and emergent quasiparticles.
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	== State-space growth ==		== State-space growth ==

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	~~<div style="display~~:~~flex; gap:24px; align-items:flex-start; max-width:1280px; clear:both;">~~		[[File:Quantum_many_body_problem_yellow.png\|thumb\|right\|320px\|Many interacting particles generate a rapidly growing quantum state space.]]
	~~<div style="flex:1 1 680px; min-width:0; line-height:1.55;">~~
	The '''quantum many-body problem''' is the challenge of describing systems containing many interacting quantum particles. Because the state space grows extremely rapidly with particle number, exact solutions are usually impossible except for small or specially structured systems.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Many-body_problem \|title=Many-body problem \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>		The '''quantum many-body problem''' is the challenge of describing systems containing many interacting quantum particles. Because the state space grows extremely rapidly with particle number, exact solutions are usually impossible except for small or specially structured systems.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Many-body_problem \|title=Many-body problem \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	Many-body physics appears in atoms, molecules, nuclei, solids, quantum fluids, plasmas, and quantum information systems. It connects microscopic quantum laws with collective behavior such as magnetism, superconductivity, phase transitions, and emergent quasiparticles.		Many-body physics appears in atoms, molecules, nuclei, solids, quantum fluids, plasmas, and quantum information systems. It connects microscopic quantum laws with collective behavior such as magnetism, superconductivity, phase transitions, and emergent quasiparticles.
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	~~[[File:Quantum_many_body_problem_yellow.png\|thumb\|360px\|Many interacting particles generate a rapidly growing quantum state space.]]~~
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	== State-space growth ==		== State-space growth ==

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	~~[[File~~:~~Quantum_many_body_problem_yellow~~.~~png\|thumb\|280px\|Many interacting particles generate a rapidly growing quantum state space.]]~~		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1280px; clear:both;">
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	The '''quantum many-body problem''' is the challenge of describing systems containing many interacting quantum particles. Because the state space grows extremely rapidly with particle number, exact solutions are usually impossible except for small or specially structured systems.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Many-body_problem \|title=Many-body problem \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>		The '''quantum many-body problem''' is the challenge of describing systems containing many interacting quantum particles. Because the state space grows extremely rapidly with particle number, exact solutions are usually impossible except for small or specially structured systems.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Many-body_problem \|title=Many-body problem \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	Many-body physics appears in atoms, molecules, nuclei, solids, quantum fluids, plasmas, and quantum information systems. It connects microscopic quantum laws with collective behavior such as magnetism, superconductivity, phase transitions, and emergent quasiparticles.		Many-body physics appears in atoms, molecules, nuclei, solids, quantum fluids, plasmas, and quantum information systems. It connects microscopic quantum laws with collective behavior such as magnetism, superconductivity, phase transitions, and emergent quasiparticles.
			</div>
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			[[File:Quantum_many_body_problem_yellow.png\|thumb\|360px\|Many interacting particles generate a rapidly growing quantum state space.]]
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	== State-space growth ==		== State-space growth ==

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			{{Quantum article nav\|previous=Physics:Quantum Exactly solvable quantum systems\|previous label=Exactly solvable quantum systems\|next=Physics:Quantum Formulas Collection\|next label=Formulas Collection}}

	[[File:Quantum_many_body_problem_yellow.png\|thumb\|280px\|Many interacting particles generate a rapidly growing quantum state space.]]		[[File:Quantum_many_body_problem_yellow.png\|thumb\|280px\|Many interacting particles generate a rapidly growing quantum state space.]]

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	[[File:Quantum_many_body_problem_yellow.png\|thumb\|280px\|Many interacting particles generate a rapidly growing quantum state space.]]		[[File:Quantum_many_body_problem_yellow.png\|thumb\|280px\|Many interacting particles generate a rapidly growing quantum state space.]]