### Abstract

As an approximation to a relativistic one-electron molecule, we study the operator {Mathematical expression} 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}∑Z_{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 {Mathematical expression}. We also show that E_{0} is an increasing function of the internuclear distances |R_{i}-R_{j}|.

Original language | English (US) |
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Pages (from-to) | 497-510 |

Number of pages | 14 |

Journal | Communications in Mathematical Physics |

Volume | 90 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 1983 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

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## Cite this

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/BF01216181