  In the Bogoliubov theory a condensate initially prepared in its ground state
described by stationary Bogoliubov vacuum and later perturbed by a
time-dependent potential or interaction strength evolves into a time-dependent
excited state which is dynamical Bogoliubov vacuum. The dynamical vacuum has a
simple diagonal form in a time-dependent orthonormal basis of single particle
modes. This diagonal representation leads to a gaussian probability
distribution for possible outcomes of density measurements in position and
momentum space. In these notes we also discuss relations with the U(1) symmetry
breaking version of the Bogoliubov theory and give two equivalent gaussian
integral representations of the dynamical vacuum state.
