Quantum Physics of Light and Matter pp 115-144 | Cite as

# Many-Body Systems

## Abstract

In this chapter we want to analyze atoms with many electrons and, more generally, systems with many interacting identical particles. We first consider the general properties of many identical particles with their bosonic or fermionic many-body wavefunctions, and the connection between spin and statistics which explains the Pauli principle and the main features of the periodic table of elements. We then discuss the Hartree-Fock approximation and also the density functional theory, historically introduced by Thomas and Fermi to model the electronic cloud of atoms and recently applied also to atomic Bose-Einstein condensates. Finally, we illustrate the Born-Oppenheimer approximation, which is very useful to treat molecules composed by many electrons in interaction with several nuclei.