Math @ Duke

Publications [#287102] of Ingrid Daubechies
Papers Published
 Daubechies, I; Lieb, EH, Oneelectron relativistic molecules with coulomb interaction
(January, 2005),
pp. 471484, Springer Verlag [doi]
(last updated on 2019/09/23)
Abstract: As an approximation to a relativistic oneelectron molecule, we study the operator H=(Δ+m2)1/2e2 Z jxRj1 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 ZiZjR iRj10. We also show that E0 is an increasing function of the internuclear distances RiR j. © 2005 SpringerVerlag Berlin Heidelberg New York.


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