Variational Analysis on the Ground State of a Charged-Boson System

The ground state of a charged-boson system is studied throughout the entire density range in a variational formalism based on the correlated wave functions. The expectation value of the Hamiltonian operator H is evaluated in the hypernetted-chain approximation using a simple trial radial distribution function which contains three variational parameters. The resulting ground-state energies are found to be higher than the exact values by 0.05 and 7.5% at high- and low-density limits, respectively. At the intermediate densities (0.01ᵣₛ100), the ground-state energies computed numerically lie slightly below the known results. It is conjectured, but not proved, that the extremum values of $〈H〉$ obtained in the present analysis are upper bounds to the exact ground-state eigenvalues.