Universal nature of van der Waals forces for Coulomb systems

  • Elliott H. Lieb
  • Walter E. Thirring


The nonrelativistic Schrödinger equation is supposed to yield a pairwise R -6 attractive interaction among atoms or molecules for large separation, R. Up to now this attraction has been investigated only in perturbation theory or else by invoking various assumptions and approximations. We show rigorously that the attraction is at least as strong as R -6 for any shapes of the molecules, independent of other features such as statistics or sign of charge of the particles. More precisely, we prove that two neutral molecules can always be oriented such that the ground-state energy of the combined system is less than the sum of the ground-state energies of the isolated molecules by a term — cR -6 provided R is larger than the sum of the diameters of the molecules. When several molecules are present, a pairwise bound of this kind is. derived. In short, we prove that in the quantum mechanics of Coulomb systems everything binds to everything else if the nuclear motion is neglected.


Dipole Moment Trial Function Coulomb System Universal Nature Effective Interaction Potential 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Elliott H. Lieb
    • 1
  • Walter E. Thirring
    • 2
  1. 1.Department of Mathematics and Department of PhysicsPrinceton UniversityPrincetonUSA
  2. 2.Institut für Theoretische PhysikUniversität WienViennaAustria

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