Math @ Duke

Publications [#287102] of Ingrid Daubechies
Papers Published
 Daubechies, I; Lieb, EH, Oneelectron relativistic molecules with coulomb interaction
(January, 2005),
pp. 471484 [doi]
(last updated on 2017/12/15)
Abstract: As an approximation to a relativistic oneelectron molecule, we study the operator H=(Δ+m 2 ) 1/2 e 2 Z j xR j  1 with Z j 0, e 2 =137.04. H is bounded below if and only if e 2 Z j > 2/π, all j. Assuming this condition, the system is unstable when e 2 ΣZ j > 2/π in the sense that E 0 =inf spec (H) →  ∞ as the R j → 0, all j. We prove that the nuclear Coulomb repulsion more than restores stability; namely E 0 +0.069e 2 Z i Z j R i R j  1 0. We also show that E 0 is an increasing function of the internuclear distances R i R j . © 2005 SpringerVerlag Berlin Heidelberg New York.


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