  We study the distribution of the $n$-th energy level for two different
one-dimensional random potentials. This distribution is shown to be related to
the distribution of the distance between two consecutive nodes of the wave
function.
  We first consider the case of a white noise potential and study the
distributions of energy level both in the positive and the negative part of the
spectrum. It is demonstrated that, in the limit of a large system
($L\to\infty$), the distribution of the $n$-th energy level is given by a
scaling law which is shown to be related to the extreme value statistics of a
set of independent variables.
  In the second part we consider the case of a supersymmetric random
Hamiltonian (potential $V(x)=\phi(x)^2+\phi'(x)$). We study first the case of
$\phi(x)$ being a white noise with zero mean. It is in particular shown that
the ground state energy, which behaves on average like $\exp{-L^{1/3}}$ in
agreement with previous work, is not a self averaging quantity in the limit
$L\to\infty$ as is seen in the case of diagonal disorder. Then we consider the
case when $\phi(x)$ has a non zero mean value.
