  We simulate three experimental methods which could be realized in the
laboratory to probe the band excitation energies and the momentum distribution
of a Bose-Einstein condensate inside an optical lattice. The values of the
excitation energies obtained in these different methods agree within the
accuracy of the simulation. The meaning of the results in terms of density and
phase deformations is tested by studying the relaxation of a phase-modulated
condensate towards the ground state.
