Variational principle for many-fermion systems

Elliott H. Lieb

Research output: Chapter in Book/Report/Conference proceedingChapter


If ψ is a determinantal variational trial function for the N-fermion Hamiltonian, H, with one- and two-body terms, then e0≤ 〈ψ, Hψ〉=E(K), where e0 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 e0≤e HF≤E(K), where eHF is the Hartree-Fock ground-state energy.

Original languageEnglish (US)
Title of host publicationThe Stability of Matter
Subtitle of host publicationFrom Atoms to Stars: Fourth Edition
PublisherSpringer Berlin Heidelberg
Number of pages4
ISBN (Print)3540420835, 9783540222125
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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