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Many-body problem

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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 or analytical calculations impractical or even impossible. 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.

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Further readingEdit

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