Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter

Lieb, Elliott H.; Thirring, Walter E.

doi:10.1103/PhysRevLett.35.687

Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter

Elliott H. Lieb
(
- Princeton U.
)
,
Walter E. Thirring
(
- Vienna U.
)

1975

3 pages

Part of The stability of matter in quantum mechanics, 401-404

Published in:

Phys.Rev.Lett. 35 (1975) 687-689,
Phys.Rev.Lett. 35 (1975) 1116 (erratum)

DOI:

10.1103/PhysRevLett.35.687,
10.1103/PhysRevLett.35.1116 (erratum)

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Abstract: (APS)

We first prove that Σ|e(V)|, the sum of the negative energies of a single particle in a potential V, is bounded above by (415π)∫|V|52. This, in turn, implies a lower bound for the kinetic energy of N fermions of the form 35(3π4)23∫ρ53, where ρ(x) is the one-particle density. From this, using the no-binding theorem of Thomas-Fermi theory, we present a short proof of the stability of matter with a reasonable constant for the bound.

FERMION: ENERGY
MANY-BODY PROBLEM
FERMION: MATTER
QUANTUM MECHANICS
ELECTRON: FORCE

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- J.Math.Phys. 8 423

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Thomas-Fermi Theory Revisited

Elliott H. Lieb
(
- IHES, Bures-sur-Yvette
)
,
Barry Simon
(
- Zurich, ETH
)

- Phys.Rev.Lett. 31 (1973) 681-683
•
DOI:
- 10.1103/PhysRevLett.31.681

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