TY - JOUR

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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U2 - 10.1103/PhysRevLett.35.687

DO - 10.1103/PhysRevLett.35.687

M3 - Article

AN - SCOPUS:0001325128

SN - 0031-9007

VL - 35

SP - 687

EP - 689

JO - Physical review letters

JF - Physical review letters

IS - 11

ER -