Many-body problem

Quantum mechanics
\Delta x\, \Delta p \ge \frac{\hbar}{2}
Introduction
Glossary · History

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.

Contents

Examples

Approaches

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