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The corrections to the mean-field approximation can be calculated using perturbation theory. The coefficient of the $(na^3)^{3/2}$ term was calculated by Lee, Huang, and Yang \cite{LHY} and the last term was first calculated by Wu \cite{wu}. Hugenholtz and Pines \cite{hp} have shown that the constant $c_1$ and the higher-order terms in the expansion are all nonuniversal...
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Hugenholtz and Pines \cite{hp} have shown that the constant $c_1$ and the higher-order terms in the expansion are all nonuniversal. Giorgini, Boronat, and Casulleras \cite{GBC} have studied the ground state of a homogeneous Bose gas by exactly solving the N-bodied Schr"odinger (to within statistical error) using a diffusion Monte Carlo method...
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