Abstract
A new application of the Bogoliubov inequality to the compressibility of a quantum or classical nonrelativistic one-component many-body system is derived. For a (two-particle) potential $\frac{\ensuremath{\lambda}}{{r}^{n}}$, the inequality can be integrated to give simple, power-law upper and lower bounds on the ground-state energy as a function of the density. Analogous results are also valid at finite temperatures and for Lennard-Jones potentials at high densities.
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