### Abstract

We first prove that |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)230ρ53, 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.

Original language | English (US) |
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Pages (from-to) | 687-689 |

Number of pages | 3 |

Journal | Physical Review Letters |

Volume | 35 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 1975 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

Lieb, E. H., & Thirring, W. E. (1975). Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter.

*Physical Review Letters*,*35*(11), 687-689. https://doi.org/10.1103/PhysRevLett.35.687