One-electron relativistic molecules with Coulomb interaction

Ingrid Daubechies, Elliott H. Lieb

Research output: Contribution to journalArticlepeer-review

67 Scopus citations


As an approximation to a relativistic one-electron molecule, we study the operator {Mathematical expression} with Zj≧0, e-2=137.04. H is bounded below if and only if e2Zj≦2/π all j. Assuming this condition, the system is unstable when e2∑Zj>2/π in the sense that E0=inf spec(H)→-∞ as the Rj→0, all j. We prove that the nuclear Coulomb repulsion more than restores stability; namely {Mathematical expression}. We also show that E0 is an increasing function of the internuclear distances |Ri-Rj|.

Original languageEnglish (US)
Pages (from-to)497-510
Number of pages14
JournalCommunications In Mathematical Physics
Issue number4
StatePublished - Dec 1983

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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