Fluctuation correction to the ground state energy density of a dilute Bose gas in the functional Schr\"{o}dinger picture

A dilute Bose gas system is studied using the functional Schr\"{o}dinger picture theory. The ground state properties are obtained by solving the infinite dimensional Schr\"{o}dinger equation variationally. It is shown that a shifted Gaussian trial wavefunctional enables us to calculate a higher order correction, which corresponds to the fluctuation contribution from the condensate. The obtained term is compared with the quantum correction arising from the low energy $3 \to 3$ scattering.