Many-body problem

Quantum mechanics

Uncertainty principle

Introduction · Mathematical formulation Background Classical mechanics Old quantum theory Interference · Bra-ket notation Hamiltonian Fundamental concepts Quantum state · Wave function Superposition · Entanglement Measurement · Uncertainty Exclusion · Duality Decoherence · Ehrenfest theorem · Tunneling Experiments Double-slit experiment Davisson–Germer experiment Stern–Gerlach experiment Bell's inequality experiment Popper's experiment Schrödinger's cat Elitzur-Vaidman bomb-tester Quantum eraser Formulations Schrödinger picture Heisenberg picture Interaction picture Matrix mechanics Sum over histories Equations Schrödinger equation Pauli equation Klein–Gordon equation Dirac equation Bohr Theory and Balmer-Rydberg Equation Interpretations Bohmian · CCC · Consistent histories · Copenhagen · Ensemble · Hidden variable theory · Many-worlds · Pondicherry · Quantum logic · Relational · Transactional Advanced topics Quantum information science scattering theory Quantum field theory Scientists Planck · Einstein · Bohr · Sommerfeld · Bose · Kramers · Heisenberg· Born · Jordan · Pauli · Dirac · de Broglie ·Schrödinger · von Neumann · Wigner · Feynman · Candlin · Bohm · Everett · Bell · Wien

This box: view • talk • edit

The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of a large number of interacting particles. Microscopic here implies that quantum mechanics has to be used to provide an accurate description of the system. A large number can be anywhere from 3 to infinity (in the case of a practically infinite, homogeneous or periodic system, such as a crystal), although three- and four-body systems can be treated by specific means (respectively the Faddeev and Faddeev-Yakubovsky equations) and are thus sometimes separately classified as few-body systems. In such a quantum system, the repeated interactions between particles create quantum correlations, or entanglement. As a consequence, the wave function of the system is a complicated object holding a large amount of information, which usually makes exact and/or analytical calculations impractical. Thus, many-body theoretical physics most often relies on a set of approximations specific to the problem at hand, and ranks among the most computationally intensive fields of science.

Examples

• Condensed matter physics (solid-state physics, nanoscience, superconductivity)
• Bose-Einstein condensation and Superfluids
• Quantum chemistry (computational chemistry, molecular physics)
• Atomic physics
• Nuclear physics (Nuclear structure, nuclear reactions, nuclear matter)
• Quantum chromodynamics (Lattice QCD, hadron spectroscopy, QCD matter, quark-gluon plasma)

Approaches

• Mean-field theory and extensions (e.g. Hartree-Fock, Random phase approximation)
• Many-body perturbation theory and Green's function-based methods
• Configuration interaction
• Coupled cluster
• Various Monte-Carlo approaches
• Density functional theory
• Lattice gauge theory

Quotes

"It would indeed be remarkable if Nature fortified herself against further advances in knowledge behind the analytical difficulties of the many-body problem."

—Max Born, 1960

Further reading

• Stephen Jenkins: The Many Body Problem and Density Functional Theory
• D. J. Thouless: The quantum mechanics of many-body systems. New York, Academic Press, 1972, ISBN 0-12-691560-1.
• A.L. Fetter and J. D. Walecka: Quantum Theory of Many-Particle Systems. New York, Dover, 2003, ISBN 0-486-42827-3.
• P. Nozières: Theory of Interacting Fermi Systems. Addison-Wesley, 1997, ISBN 0-201-32824-0.
• R. D. Mattuck: A guide to Feynman diagrams in the many-body problem. New York, McGraw-Hill, 1976, ISBN 0-07-040954-4

This quantum mechanics-related article is a stub. You can help Wikipedia by expanding it. v • d • e