Abstract
The idea of trying to represent the ground state (and perhaps some of the excited states as well) of atomic, molecular, and solid state systems in terms of the diagonal part of the one-body reduced density matrix ρ(x) is an old one. It goes back at least to the work of Thomas [1] and Fermi [2] in 1927. In 1964 the idea was conceptually extended by Hohenberg and Kohn (HK) [3]. Since then many variations on the theme have been introduced. As the present article is not meant to be a review, I shall not attempt to list the papers in the field. Some recent examples of applications are Refs. 4 and 5. Some recent examples of theoretical papers which will play a role here are Refs. 6–12. A bibliography can be found in the recent review article of Bamzai and Deb [13].
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References
L.H. Thomas, Proc. Camb. Phil. Soc. 23: 542 (1927).
E. Fermi, Rend. Accad. Naz. Lincei 6: 602 (1927).
P.Hohenberg and W. Kohn, Phys. Rev. B136: 864 (1964).
M.M. Morell, R.G. Parr and M. Levy, J. Chem. Phys. 62: 549 (1975).
R.G. Parr, S. Cadre and L.J. Bartolotti, Proc. Natl. Acad. Sci. 76: 2522 (1979).
R.A. Donnelly and R.G. Parr, J. Chem. Phys. 69: 4431 (1978).
H. Englisch and R. Englisch, “Hohenberg-Kohn theorem and non-vrepresentable densities”, Physica A, to be published.
T.L. Gilbert, Phys. Rev. B6: 211 (1975).
J.E. Harriman, Phys. Rev. A6: 680 (1981).
M. Levy, Proc. Natl. Acad. Sci. USA 76: 6062 (1979).
M. Levy, Phys. Rev. A26: 1200 (1982).
S.M. Valone, J. Chem. Phys. 73:1344 (1980); ibid. 73: 4653 (1980).
A.S. Bamazai and B.M. Deb, Rev. Mod. Phys. 53:95 (1981). Erratum, 53: 593 (1981).
E.H. Lieb and B. Simon, Adv. Math. 23:22 (1977) See also Thomas-Fermi theory revisited, Phys. Lett.31:681 (1973. See also Refs. 16 and 25.
M. Hoffmann-Ostenhof and T. Hoffmann-Ostenhof, Phys. Rev. A16: 1782 (1977).
E.H. Lieb, Rev. Mod. Phys. 48: 553 (1976).
N.H. March and W.H. Young, Proc. Phys. Soc. 72: 182 (1958).
M. Reed and B. Simon, Methods of Modern Mathematical Physics (Academic. New York,1978), Vol. 4.
S. Mazur, Studia Math. 4: 70 (1933).
R.B.Israel, Convexity in the Theory of Lattice Gases(Princeton NJ. (1979).
E.H. Lieb and W.E. Thirring, “Inequalities for the moments of the eigenvalues of the Schrödinger hamiltonian and their relation to Sobolev inequalities”, in Studies in Mathematical Physics, E.H. Lieb, B. Simon and A.S. Wightman, Eds. (Princeton U.P., Princeton, N.J. 1976). See also Phys. Rev. Lett. 687 (1975); Errata 35:1116 (1975).
E.H. Lieb, Am. Math. Soc. Proc. Symp. Pure Math. 36: 241 (1980).
E.H. Lieb, Phys. Lett. A70: 444 (1979).
E.H. Lieb and S. Oxford, Int. J. Quantum Chem. 19: 427 (1981).
È.H. Lieb, Rev. Mod. Phys. 53:603 (1981); Errata, 54: 311 (1982).
E.H. Lieb, Phys. Rev. Lett.46:457 (1981); Erratum, 47_69 (1981).
J.K. Percus, Int. J. Quantum Chem. 13: 89 (1978).
R.A. Adams, Sobolev Spaces (Avademic Press, New York)(1975).
W. Fenchel, Can. J. Math. 1: 23 (1949).
W. Kohn and L.J. Sham, Phys. Rev. A140: 1133 (1965).
H. Brezis, Analyse Functionelle, Theorie et Applications, Masson, Paris (1983).
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© 1985 Plenum Press, New York
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Lieb, E.H. (1985). Density Functionals for Coulomb Systems. In: Dreizler, R.M., da Providência, J. (eds) Density Functional Methods In Physics. NATO ASI Series, vol 123. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0818-9_3
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