## Abstract

A modification of the Rayleigh-Ritz variational principle is described which makes possible a calculation of the energy, wave function, and pair distribution function f$_{12}\equiv$ f(X$_1$, X$_2$) of a Bose fluid, such as liquid $^4$He, at absolute zero. The assumptions made are: (i) two-body interactions with potential U$_{ij}$, (ii) trial wave functions of the form $\Pi_i\neq j$ exp $\phi_{ij}$, and (iii) the Kirkwood `superposition' approximation. Under these approximations, the expectation energy is $E=\frac e{1}{2}n^2\int\int d^3x_1d^3x_2f_{12}{U_{12}-h^2 m^{-1}[(\nabla^2_1\phi_{12})+(\nabla_1\phi_{12})^2+n\int d^3x_3f_{13}f_{23}\nabla_1\phi_{12}\cdot\nabla_1\phi_{13}]},$ where n$\equiv$N/V. It is shown here that making E stationary with respect to independent variations in f and $\phi$ corresponds to simultaneously applying the ordinary Rayleigh-Ritz principle and solving the Born-Green-Yvon integral equation for f. The method is illustrated by reproducing Bogolyubov's results for the case where U is small. The case where U is large must be dealt with numerically, but transformations for simplifying the computations are given here.