Theory of inhomogeneous quantum systems. I. Static properties of Bose fluids

Abstract

We develop a variational theory for the determination of the ground-state properties of an inhomogeneous Bose fluid at zero temperature. Euler-Lagrange equations are derived for the one- and two-body correlations, and systematic approximation methods are physically motivated. It is shown that the optimized variational method provides a self-consistent approximate summation of ladder and ring diagrams. Numerical applications are presented for the density profile, distribution functions, energy, and chemical potential of films of $^{4}\mathrm{He}$ atoms. Both the bulk and surface energies are calculated and found to be in fair agreement with experiments.