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Variational Principle for Many-Fermion Systems

  • Elliott H. Lieb

Abstract

If ψ is a determinantal variational trial function for the N-fermion Hamiltonian, H, with one- and two-body terms, then e 0 ⩽ 〈 ψ,Hψ〉= E(K), where e 0 is the ground-state energy, K is the one-body reduced density matrix of ψ, and E(K) is the well-known expression in terms of direct and exchange energies. If an arbitrary one-body K is given, which does not come from a determinantal ψ, then E(K) ⩾ e 0 does not necessarily hold. It is shown, however, that if the two-body part of H is positive, then in fact e 0e HFE(K), where e HF is the Hartree-Fock ground-state energy.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

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

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