  In Gaudin (1960), Michel Gaudin showed the Wick's theorem at finite
temperature using a diagonal Hamiltonian. We extend the Gaudin's prove for a
statistical density operator which depend on a quadratic Hamiltonian. To
illustrate the utility of the theorem, we evaluate the ratio
$\sqrt{[<\hat{N}^2>-<\hat{N}>^2]/<\hat{N}>}$ of a homogeneous weakly
interacting Bose gas at temperature below the Bose-Einstein condensation
temperature. At this condition, the quadratic Hamiltonian approximation is
valued and, in this evaluation, we show the sub-Poissonian behaviour of the
fundamental state distribution at zero temperature.
