Ground-State Energy of a Finite System of Charged Particles

A trial wavefunction of superconducting type is postulated for the ground state of a system of N positive and N negative charges with Coulomb interactions in the absence of any exclusion principle. The ground‐state binding energy is rigorously proved to be greater than ${\mathrm{AN}}^{\frac{7}{5}}$ Ry, where A is an absolute constant. Results of earlier perturbation‐theoretic calculations for an infinite system are confirmed. The author, with A. Lenard, has previously proved that the exclusion principle, holding for particles with one sign of charge only, is a sufficient condition for the stability of matter; the present paper shows that the exclusion principle is also necessary for stability.