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 (415π)∫|V|5/2. This, in turn, implies a lower bound for the kinetic energy of N fermions of the form 3/5(3π4)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.
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Lieb et al. (1975) studied this question.
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