The Stability of Matter

  • E. H. Lieb
Conference paper
Part of the Acta Physica Austriaca book series (FEWBODY, volume 17/1977)


An outline is presented of the proofs of three basic facts about quantum-mechanical Coulomb systems: (i) atoms have finite ground state energies; (ii) the energy of bulk matter saturates; (iii) the thermodynamic limit exists.


Ground State Energy Thermodynamic Limit Uncertainty Principle Coulomb Force Total Particle Number 
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.
    S.L. Sobolev, Mat. Sb. 46, 471, 1938. See also S.L, Sobolev, Amer. Math. Soc. Trans 1. of Monographs, 7, 1963.Google Scholar
  2. 2.
    T. Kato, Trans. Amer. Math. Soc. 70, 195, 1951.MathSciNetMATHGoogle Scholar
  3. 3.
    F.J. Dyson and A. Lenard, J. Math. Phys. 8, 423, 1967. See also A. Lenard and F.J. Dyson, J. Math. Phys. 9, 698, 1968.MathSciNetMATHGoogle Scholar
  4. 4.
    E.H. Lieb and W.E. Thirring, Phys. Rev. Lett. 35, 687, 1975? Errata: Phys. Rev. Lett, 3J5, 1116, 1975. For more details on kinetic energy inequalities and their application, see also 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: Essays in Honor of Valentine Bargmann, E.H. Lieb, B. Simon and A.S. Wightman editors, Princeton University Press, 1976.Google Scholar
  5. 5.
    F.J. Dyson, J. Math. Phys. 8, 1538, 1967.MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    E.H. Lieb and B. Simon, Adv. in Math. 1977, in press. See also E.H. Lieb and B. Simon, Phys. Rev. Lett. 33, 681, 1973.Google Scholar
  7. 7.
    E.H. Lieb and J.L. Lebowitz, Adv. in Math. 9, 316, 19 72. See also J.L. Lebowitz and E.H. Lieb, Phys. Rev. Lett. 22, 631, 1969.Google Scholar
  8. 8.
    E.H. Lieb, Rev. Mod. Phys. October 1976.Google Scholar
  9. 9.
    W. Heisenberg, Zeits. Phys. 43, 172, 1927.ADSCrossRefGoogle Scholar
  10. 10.
    G. Rosen, Siam J. Appl. Math. 21, 30, 1971.MATHGoogle Scholar
  11. 11.
    E.H. Lieb, Bull. Amer. Math. Soc. 1976, in press.Google Scholar
  12. 12.
    E. Teller, Rev. Mod. Phys. 34, 627, 1962.ADSMATHCrossRefGoogle Scholar
  13. 13.
    E.H. Lieb and H. Narnhofer, J. Stat. Phys. 12, 291, 1975. Erratum: J. Stat. Phys. 14, No. 5, 1976.Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • E. H. Lieb
    • 1
  1. 1.Dept. of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

Personalised recommendations