Inequalities pp 377-388 | Cite as

Coherent States as a Tool for Obtaining Rigorous Bounds

  • Elliott H. Lieb


This talk reviews some of the ways in which coherent states can be used to give rigorous bounds for quantities of physical interest and, in certain cases, can yield exact asymptotic formulas. Three main topics will be discussed.


Coherent State Ground State Energy Coulomb System Rigorous Bound Wehrl Entropy 
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.
    F.A. Berezin, Covariant and contravariant symbols of operators, Izv. Akad. SSSR Ser. Mat. 6 (1972) 1134–1167.MathSciNetGoogle Scholar
  2. 2.
    E.H. Lieb, The classical limit of quantum spin systems, Commun. Math. Phys. 31 (1973) 327–340.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    E.H. Lieb and J.P. Solovej, Quantum coherent operators: A generalization of coherent states, Lett. Math. Phys. 22 (1991) 145–154.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    K. Hepp and E.H. Lieb, On the superradiant phase transition for molecules in a quantized radiation field, Ann. of Phys. (NY) 76 (1973) 360–404.MathSciNetCrossRefGoogle Scholar
  5. 5.
    K. Hepp and E.H. Lieb, The equilibrium statistical mechanics of matter interacting with the quantized radiation field, Phys. Rev. A8 (1973) 2517–2525.MathSciNetGoogle Scholar
  6. 6.
    E.H. Lieb and B. Simon, Thomas-Fermi theory of atoms, molecules and solids, Adv. in Math. 23 (1977) 22–116.MathSciNetCrossRefGoogle Scholar
  7. 7.
    E.H. Lieb, Thomas-Fermi and related theories of atoms and molecules, Rev. Mod. Phys. 53 (1981) 603–641; errata 54 (1981) 311. See Sect. V.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    W. Thirring, A lower bound with the best possible constants for Coulomb Hamiltonians, Commun. Math. Phys. 79 (1981) 1–7.MathSciNetCrossRefGoogle Scholar
  9. 9.
    E.H. Lieb, A variational principle for many-fermion systems, Phys. Rev. Lett. 46 (1981) 457–459; errata 47 (1981) 69.MathSciNetCrossRefGoogle Scholar
  10. 10.
    V. Bach, Error bounds for the Hartree-Fock energy of atoms and molecules, Commun. Math. Phys. 147 (1992) 527–548.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    E.H. Lieb and S. Oxford, An improved lower bound on the indirect Coulomb energy, Int. J. Quant. Chem. 19 (1981) 427–439.CrossRefGoogle Scholar
  12. 12.
    A. Wehrl, On the relation between classical and quantum-mechanical entropy, Rept. Math. Phys. 16 (1979) 353–358.MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    E.H. Lieb, Some convexity and subadditivity properties of entropy, Bull. Amer. Math. Soc. 81 (1975) 1–13.MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    E.H. Lieb, Proof of an entropy conjecture of Wehrl, Commun. Math. Phys. 62 (1978) 35–41.MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    E.H. Lieb, Integral bounds for radar ambiguity functions and Wigner distributions, J. Math. Phys. 31 (1990) 594–599.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Elliott H. Lieb
    • 1
  1. 1.Department of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

Personalised recommendations