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Many-body problem

The many-body problem is a general name for a vast category of physical problems pertaining to the properties of microscopic systems made of many 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 three 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.