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Publications [#287102] of Ingrid Daubechies

Papers Published

  1. Daubechies, I; Lieb, EH, One-electron relativistic molecules with coulomb interaction (January, 2005), pp. 471-484 [doi]
    (last updated on 2017/12/15)

    Abstract:
    As an approximation to a relativistic one-electron molecule, we study the operator H=(-Δ+m 2 ) 1/2 -e 2 Z j |x-R 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 Springer-Verlag Berlin Heidelberg New York.

 

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