A fundamental paradox of classical physics is why matter, which is held together by Coulomb forces, does not collapse. The resolution is given here in three steps. First, the stability of atom is demonstrated, in the framework of nonrelativistic quantum mechanics. Next the Pauli principle, together with some facts about Thomas—Fermi theory, is shown, to account for the stability (i.e., saturation) of bulk matter. Thomas—Fermi theory is developed in some detail because, as is also pointed out, it is the asymptotically correct picture of heavy atoms and molecules (in the Z→∞ limit). Finally, a rigorous version of screening is introduced to account for thermodynamic stability.


Thermodynamic Limit Coulomb Potential Nuclear Charge Coulomb Force Small Ball 
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© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Elliott H. Lieb
    • 1
  1. 1.Department of Mathematics and Department of PhysicsPrinceton UniversityPrincetonUSA

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