Math @ Duke

Publications [#287120] of Ingrid Daubechies
Papers Published
 Daubechies, I; Lieb, EH, Oneelectron relativistic molecules with Coulomb interaction,
Communications in Mathematical Physics, vol. 90 no. 4
(1983),
pp. 497510, ISSN 00103616 [doi]
(last updated on 2017/12/16)
Abstract: As an approximation to a relativistic oneelectron molecule, we study the operator {Mathematical expression} with Zj≧0, e2=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 RiRj. © 1983 SpringerVerlag.


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