Bound for the kinetic energy of fermions which proves the stability of matter

Elliott Lieb, Walter E. Thirring

Research output: Chapter in Book/Report/Conference proceedingChapter

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∫ρ5/3, 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 languageEnglish (US)
Title of host publicationThe Stability of Matter
Subtitle of host publicationFrom Atoms to Stars: Fourth Edition
PublisherSpringer Berlin Heidelberg
Pages401-404
Number of pages4
ISBN (Print)3540420835, 9783540222125
DOIs
StatePublished - 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