Abstract
If ψ is a determinantal variational trial function for the JV-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) ≥ e0 does not necessarily hold. It is shown, however, that if the two-body part of H is positive, then in fact e 0 ≤ eHF≤ E(K), where eHF is the Hartree-Fock ground-state energy.
An erratum to this chapter is available at http://dx.doi.org/10.1007/978-3-662-04360-8_50
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References
Elliott H. Lieb, Phys. Rev. Lett. 46, 457 (1981),
Elliott H. Lieb, Phys. Rev. Lett. and 47, 69(E) (1981).
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© 2001 Springer-Verlag Berlin Heidelberg
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Lieb, E.H. (2001). Variational Principle for Many-Fermion Systems. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04360-8_19
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DOI: https://doi.org/10.1007/978-3-662-04360-8_19
Publisher Name: Springer, Berlin, Heidelberg
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