We study the energy distribution of maxima and minima of a simple one-dimen
sional disordered Hamiltonian. We find that in systems with short-range cor
related disorder there is energy separation between maxima and minima, such
that at fixed energy only one kind of stationary point is dominant in numb
er over the other. On the other hand, in the case of systems with long-rang
e correlated disorder maxima and minima an completely mixed. [S1063-651X(99
)14703-2].