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

1975/09/15 by Élliott H. Lieb, Walter Thirring · 8 citations
Physics and Astronomy · Mathematics · Chemistry · #Advanced Thermodynamics and Statistical Mechanics #Spectral Theory in Mathematical Physics #Chemical Thermodynamics and Molecular Structure

paper · doi:10.1103/physrevlett.35.687

openalex publication_date 1975/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/19

Abstract

We first prove that \ensuremathΣ|e(V)|, the sum of the negative energies of a single particle in a potential V, is bounded above by (\frac415\ensuremathπ)\ensuremath∫|V|^(5)/(2). This, in turn, implies a lower bound for the kinetic energy of N fermions of the form (3)/(5)(\frac3\ensuremathπ4)^(2)/(3)\ensuremath∫\ensuremathρ^(5)/(3), where \ensuremathρ(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.

Citations

• The Thomas-Fermi theory of atoms, molecules and solids
• Search for charm
• The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei

Cited by

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• A Blaschke-type condition and its application to complex Jacobi matrices
• The Nonlinear Schrödinger Equation for Orthonormal Functions: Existence of Ground States
• A positive density analogue of the Lieb–Thirring inequality
• The Nonlinear Schrödinger Equation for Orthonormal Functions II: Application to Lieb–Thirring Inequalities
• Hartree corrections in a mean-field limit for fermions with Coulomb interaction*
• Freeman Dyson [wikipedia]