Publications [#287102] of Ingrid Daubechies

Papers Published

1. Daubechies, I; Lieb, EH, One-electron relativistic molecules with coulomb interaction (January, 2005), pp. 471-484, Springer Verlag [doi]
   (last updated on 2025/04/04)

   Abstract:
   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.