One-electron relativistic molecules with Coulomb interaction

Ingrid Daubechies; Elliott H. Lieb

doi:10.1007/BF01216181

One-electron relativistic molecules with Coulomb interaction

Ingrid Daubechies, Elliott H. Lieb

Mathematics

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

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 e²Z_j≦2/π all j. Assuming this condition, the system is unstable when e²∑Z_j>2/π in the sense that E₀=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 E₀ is an increasing function of the internuclear distances |R_i-R_j|.

Original language	English (US)
Pages (from-to)	497-510
Number of pages	14
Journal	Communications In Mathematical Physics
Volume	90
Issue number	4
DOIs	https://doi.org/10.1007/BF01216181
State	Published - Dec 1983

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01216181

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title = "One-electron relativistic molecules with Coulomb interaction",

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|.",

author = "Ingrid Daubechies and Lieb, {Elliott H.}",

year = "1983",

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T1 - One-electron relativistic molecules with Coulomb interaction

AU - Daubechies, Ingrid

AU - Lieb, Elliott H.

PY - 1983/12

Y1 - 1983/12

N2 - 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|.

AB - 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|.

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SP - 497

EP - 510

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 4

ER -

One-electron relativistic molecules with Coulomb interaction

Abstract

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