  We report on the measurement of the spectral functions of noninteracting
ultracold atoms in a three-dimensional disordered potential resulting from an
optical speckle field. Varying the disorder strength by 2 orders of magnitude,
we observe the crossover from the "quantum" perturbative regime of low disorder
to the "classical" regime at higher disorder strength, and find an excellent
agreement with numerical simulations. The method relies on the use of
state-dependent disorder and the controlled transfer of atoms to create
well-defined energy states. This opens new avenues for experimental
investigations of three-dimensional Anderson localization.
