We discuss the localization behavior of quantum particles in a one-dimensio
nal Anderson model with correlated and uncorrelated random potentials. We a
re interested in the question if a localization-delocalization transition i
n these systems can occur and what the conditions are that allow for such a
transition between localized and extended states. For the particular case
of self-affine potential landscapes we show that a localization-delocalizat
ion transition reported recently only occurs, if the variance of the potent
ial fluctuations is kept fixed for all system sizes. If no constraints on t
he variance are imposed, a new type of "strong" localization occurs in self
-affine systems, All states are strongly localized in a way different from
the usual Anderson localized states. (C) 2000 Elsevier Science B.V. All rig
hts reserved.