### Abstract

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 (4/15π)∫|V| ^{5/2}. This, in turn, implies a lower bound for the kinetic energy of N fermions of the form 3/5(3π)/4)^{2/3}∫ρ^{5/3}, 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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Title of host publication | The Stability of Matter |

Subtitle of host publication | From Atoms to Stars: Fourth Edition |

Publisher | Springer Berlin Heidelberg |

Pages | 401-404 |

Number of pages | 4 |

ISBN (Print) | 3540420835, 9783540222125 |

DOIs | |

State | Published - Jan 1 2005 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

Lieb, E., & Thirring, W. E. (2005). Bound for the kinetic energy of fermions which proves the stability of matter. In

*The Stability of Matter: From Atoms to Stars: Fourth Edition*(pp. 401-404). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-27056-6_28