Publications [#287120] of Ingrid Daubechies

Papers Published

1. Daubechies, I; Lieb, EH, One-electron relativistic molecules with Coulomb interaction, Communications in Mathematical Physics, vol. 90 no. 4 (December, 1983), pp. 497-510, Springer Nature, ISSN 0010-3616
   (last updated on 2024/04/19)

   Abstract:
   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|. © 1983 Springer-Verlag.