One-electron relativistic molecules with coulomb interaction

Journal Article (Chapter)

As an approximation to a relativistic one-electron molecule, we study the operator H=(-Δ+m2)1/2-e2 Z j|x-Rj|-1 with Zj0, e -2=137.04. H is bounded below if and only if e2 Z j>2/π, all j. Assuming this condition, the system is unstable when e2ΣZj>2/π in the sense that E 0=inf spec (H) → - ∞ as the Rj → 0, all j. We prove that the nuclear Coulomb repulsion more than restores stability; namely E0+0.069e2 ZiZj|R i-Rj|-10. We also show that E0 is an increasing function of the internuclear distances |Ri-R j|. © 2005 Springer-Verlag Berlin Heidelberg New York.

Full Text

Duke Authors

Cited Authors

  • Daubechies, I; Lieb, EH

Published Date

  • January 1, 2005

Start / End Page

  • 471 - 484

Digital Object Identifier (DOI)

  • 10.1007/3-540-27056-6_33

Citation Source

  • Scopus