Correlation functions for a Bose-Einstein condensate in the Bogoliubov approximation

In this article we introduce a differential equation for the first order correlation function G ⁽¹⁾ of a Bose-Einstein condensate at T = 0. The Bogoliubov approximation is used. Our approach points out directly the dependence on the physical parameters. Furthermore it suggests a numerical method to calculate G ⁽¹⁾ without solving an eigenvector problem. The G ⁽¹⁾ equation is generalized to the case of non zero temperature. Received 20 September 2000