Physics:Quantum many-body problem - Revision history

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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}}		{{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}}
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	[[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.]]
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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.
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	== State-space growth ==		== State-space growth ==

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

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{{Short description|Problem of describing interacting systems with many quantum particles}}
{{Quantum book backlink|Mathematical structure and systems}}

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

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.

== 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.

This growth makes approximation methods central. Mean-field theory, perturbation theory, density functional theory, tensor networks, Monte Carlo methods, and effective models are all ways to reduce or reorganize the complexity.

== Collective behavior ==
Many-body systems often display properties not obvious from individual particles alone. Examples include [[Physics:Quantum Superconductivity|superconductivity]], [[Physics:Quantum spin liquid|spin liquids]], Fermi liquids, and topological phases.

The many-body problem is therefore both a technical challenge and a source of new physical phenomena.

== See also ==
* [[Physics:Quantum Approximation Methods]]
* [[Physics:Quantum Statistical mechanics]]
* [[Physics:Quantum Fock space]]
* [[Physics:Quantum Exchange interaction]]

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

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum many-body problem|1}}