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

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 He4 atoms. Both the bulk and surface energies are calculated and found to be in fair agreement with experiments.