## One-electron relativistic molecules with Coulomb interaction

Publication
, Journal Article

Daubechies, I; Lieb, EH

Published in: Communications in Mathematical Physics

December 1, 1983

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.

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## Published In

Communications in Mathematical Physics

## DOI

## EISSN

1432-0916

## ISSN

0010-3616

## Publication Date

December 1, 1983

## Volume

90

## Issue

4

## Start / End Page

497 / 510

## Related Subject Headings

- Mathematical Physics
- 5107 Particle and high energy physics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0105 Mathematical Physics
- 0101 Pure Mathematics

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Daubechies, I., & Lieb, E. H. (1983). One-electron relativistic molecules with Coulomb interaction.

*Communications in Mathematical Physics*,*90*(4), 497–510. https://doi.org/10.1007/BF01216181Daubechies, I., and E. H. Lieb. “One-electron relativistic molecules with Coulomb interaction.”

*Communications in Mathematical Physics*90, no. 4 (December 1, 1983): 497–510. https://doi.org/10.1007/BF01216181.Daubechies I, Lieb EH. One-electron relativistic molecules with Coulomb interaction. Communications in Mathematical Physics. 1983 Dec 1;90(4):497–510.

Daubechies, I., and E. H. Lieb. “One-electron relativistic molecules with Coulomb interaction.”

*Communications in Mathematical Physics*, vol. 90, no. 4, Dec. 1983, pp. 497–510.*Scopus*, doi:10.1007/BF01216181.Daubechies I, Lieb EH. One-electron relativistic molecules with Coulomb interaction. Communications in Mathematical Physics. 1983 Dec 1;90(4):497–510.

## Published In

Communications in Mathematical Physics

## DOI

## EISSN

1432-0916

## ISSN

0010-3616

## Publication Date

December 1, 1983

## Volume

90

## Issue

4

## Start / End Page

497 / 510

## Related Subject Headings

- Mathematical Physics
- 5107 Particle and high energy physics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0105 Mathematical Physics
- 0101 Pure Mathematics