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Recent mathematical results on the quantum modeling of crystals

  • I. Catto
  • P.-L. Lions
  • C. Le Bris
Part of the Lecture Notes in Chemistry book series (LNC, volume 74)

Abstract

We describe in this paper a strategy, the so-called thermodynamic limit process, to build in a rigorous mathematical manner the quantum-mechanical models for the ground-state energy of solid crystals. These models are the analogues for the solid state of well-known models issued from Quantum Chemistry, namely Thomas-Fermi, Hartree and Hartree-Fock type models. We shall present a broad overview on recent mathematical studies on this topic.

Keywords

Thermodynamic Limit Quantum Modeling Periodic Model Bloch Wave Wannier Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • I. Catto
    • 1
  • P.-L. Lions
    • 1
  • C. Le Bris
    • 2
  1. 1.CEREMADE (UMR CNRS 7534)Université Paris-DauphineParis Cedex 16France
  2. 2.CERMICSEcole Nationale des Ponts et ChausséesMarne-La- Vallée CedexFrance

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