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Zbl 0623.46041
Fefferman, Charles
The N-body problem in quantum mechanics. (English)
[J] Commun. Pure Appl. Math. 39, Suppl., S67-S109 (1986). ISSN 0010-3640

Let us consider a system of N electrons and M nuclei interacting by inverse-square forces. Under suitable temperature and pressure this system may become a crystal or a gas. The physical laws that govern such a system have been known for a long time. But why these states? Understanding why those laws lead to the observed behavior of matter is a mthematical challenge. \par Embarked for a long time on a program to prove that electrons and nuclei can form atomic and molecular gases the author in this very interesting paper explains what he has succeeded in proving and what remains to be done. \par His main theorem is that up to some accuracy there exists a temperature and density such that in a sufficiently large box the Gibbs measure describes a gas of hydrogen atoms. A very difficult result to prove.
[P.Hillion]

MSC 2000:: *46N99 Appl. of functional analysis
82B40 Kinetic theory of gases
70F10 n-body problem

Keywords: Gibbs distribution; system of N electrons and M nuclei interacting by inverse-square forces; Gibbs measure; gas of hydrogen atoms

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