The Positivity of the Pressure in Thomas Fermi Theory

  • R. Benguria
  • E. H. Lieb


We prove the positivity of the pressure and compressibility for neutral systems in the Thomas-Fermi theory of molecules. Our results include some new properties of the Thomas-Fermi potential and a proof that the kinetic energy is superadditive.


Neutral System Bounded Continuous Function Neutral Case Nuclear Repulsion Uniform Dilation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lieb, E. H., Simon, B.: Advan. Math. 23, 22–116 (1977)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Lieb, E. H., Simon, B.: Phys. Rev. Letters 31, 681–683 (1973)ADSCrossRefGoogle Scholar
  3. Lieb, E. H.: Proc. Int. Congress of Math., Vancouver (1974)Google Scholar
  4. Lieb, E. H.: Rev. Mod. Phys. 48, 553–569 (1976)MathSciNetADSCrossRefGoogle Scholar
  5. 3.
    Benguria, R., Lieb, E. H.: Ann. Phys. (N.Y.) 110, 34–45 (1978)MathSciNetADSCrossRefGoogle Scholar
  6. 4.
    Balàsz, N.: Phys. Rev. 156, 42–47 (1967)ADSCrossRefGoogle Scholar
  7. 5.
    Teller, E.: Rev. Mod. Phys. 34, 627–631 (1962)ADSMATHCrossRefGoogle Scholar
  8. 6.
    Reed, M., Simon, B.: Methods of modern mathematical physics. Vol. II, Fourier analysis and selfadjointness. New York: Academic Press 1975Google Scholar
  9. 7.
    Hille, E.: Proc. Nat. Acad. Sci. 62, 7–10 (1969)MathSciNetADSMATHCrossRefGoogle Scholar
  10. 8.
    Rockafellar, R. T.: Convex analysis. Princeton: University Press 1970MATHGoogle Scholar
  11. 9.
    Faris, W.: Duke Math. J. 43, 365–372 (1976)MathSciNetMATHCrossRefGoogle Scholar
  12. 10.
    Strichartz, R. S.: J. Math. Mech. 16, 1031–1060 (1967)MathSciNetMATHGoogle Scholar
  13. 11.
    Lieb, E. H., Simon, B.: Monotonicity of the electronic contribution to the Born-Oppenheimer energy. J. Phys. B (London) I1, L537–542 (1979)Google Scholar
  14. 12.
    Brezis, H. Lieb, E. H.: Long range atomic potentials in Thomas-Fermi theory. Commun. math. Phys. (submitted)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • R. Benguria
    • 1
    • 3
  • E. H. Lieb
    • 2
  1. 1.Department of PhysicsPrinceton UniversityPrincetonUSA
  2. 2.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA
  3. 3.Department of PhysicsUniversidad de ChileSantiagoChile

Personalised recommendations