One-electron relativistic molecules with coulomb interaction

Ingrid Daubechies, Elliott H. Lieb

Research output: Chapter in Book/Report/Conference proceedingChapter


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|.

Original languageEnglish (US)
Title of host publicationThe Stability of Matter
Subtitle of host publicationFrom Atoms to Stars: Fourth Edition
PublisherSpringer Berlin Heidelberg
Number of pages14
ISBN (Print)3540420835, 9783540222125
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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