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

Elliott H. Lieb; Walter E. Thirring

doi:10.1103/PhysRevLett.35.687

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

Elliott H. Lieb
, Walter E. Thirring

Mathematics

Research output: Contribution to journal › Article › peer-review

301 Scopus citations

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)
Pages (from-to)	687-689
Number of pages	3
Journal	Physical review letters
Volume	35
Issue number	11
DOIs	https://doi.org/10.1103/PhysRevLett.35.687
State	Published - 1975

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1103/PhysRevLett.35.687

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title = "Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter",

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.",

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

note = "Funding Information: Work supported by the U. S. National Science Foundation under Grant No. MPS 71-03375-A03 at the Massachusetts Institute of Technology. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.",

year = "1975",

doi = "10.1103/PhysRevLett.35.687",

language = "English (US)",

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journal = "Physical review letters",

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T1 - Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter

AU - Lieb, Elliott H.

AU - Thirring, Walter E.

N1 - Funding Information: Work supported by the U. S. National Science Foundation under Grant No. MPS 71-03375-A03 at the Massachusetts Institute of Technology. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1975

Y1 - 1975

N2 - 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.

AB - 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.

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UR - https://www.scopus.com/pages/publications/0001325128#tab=citedBy

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DO - 10.1103/PhysRevLett.35.687

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EP - 689

JO - Physical review letters

JF - Physical review letters

IS - 11

ER -

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

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