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Inequalities pp 269-303 | Cite as

Density Functionals for Coulomb Systems

  • Elliott H. Lieb

Abstract

This paper has three aims: (i) To discuss some of the mathematical connections between N-particle wave functions Ψ and their single-particle densities p(x). (ii) To establish some of the mathematical underpinnings of “universal density functional” theory for the ground state energy as begun by Hohenberg and Kohn. We show that the HK functional is not defined for all p and we present several ways around this difficulty. Several less obvious problems remain, however, (iii) Since the functional mentioned above is not computable, we review examples of explicit functionals that have the virtue of yielding rigorous bounds to the energy.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

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

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