  We propose to use quantum tomography to characterize the state of a perturbed
Bose-Einstein condensate. We assume knowledge of the number of particles in the
zero-wave number mode and of density distributions in space at different times,
and we treat the condensate in the Bogoliubov approximation. For states that
can be treated with the Gross-Pitaevskii equation, we find that the
reconstructed density operator gives excellent predictions of the second
moments of the atomic creation- and annihilation operators, including the
one-body density matrix. Additional inclusion of the momentum distribution at
one point of time enables somewhat reliable predictions to be made for the
second moments for mixed states, making it possible to distinguish between
coherent and thermal perturbations of the condensate. Finally, we find that
with observation of the zero-wave number mode's anomalous second moment the
reconstructed density operator gives reliable predictions of the second moments
of locally amplitude squeezed states.
