  We study the single particle density of states of a one-dimensional speckle
potential, which is correlated and non-Gaussian. We consider both the repulsive
and the attractive cases. The system is controlled by a single dimensionless
parameter determined by the mass of the particle, the correlation length and
the average intensity of the field. Depending on the value of this parameter,
the system exhibits different regimes, characterized by the localization
properties of the eigenfunctions. We calculate the corresponding density of
states using the statistical properties of the speckle potential. We find good
agreement with the results of numerical simulations.
