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

Elliott H. Lieb; Walter E. Thirring

doi:10.1007/3-540-27056-6_28

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

Elliott H. Lieb, Walter E. Thirring

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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)
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	https://doi.org/10.1007/3-540-27056-6_28
State	Published - 2005

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

Access to Document

10.1007/3-540-27056-6_28

Cite this

@inbook{ac9dece659f84f8d929771bdf673d3bc,

title = "Bound for the kinetic energy of fermions which proves the stability of matter",

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.",

author = "Lieb, {Elliott H.} and Thirring, {Walter E.}",

year = "2005",

doi = "10.1007/3-540-27056-6_28",

language = "English (US)",

isbn = "3540420835",

pages = "401--404",

booktitle = "The Stability of Matter",

publisher = "Springer Berlin Heidelberg",

}

TY - CHAP

T1 - Bound for the kinetic energy of fermions which proves the stability of matter

AU - Lieb, Elliott H.

AU - Thirring, Walter E.

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84892273533&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892273533&partnerID=8YFLogxK

U2 - 10.1007/3-540-27056-6_28

DO - 10.1007/3-540-27056-6_28

M3 - Chapter

AN - SCOPUS:84892273533

SN - 3540420835

SN - 9783540222125

SP - 401

EP - 404

BT - The Stability of Matter

PB - Springer Berlin Heidelberg

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this