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We study the distribution of the $n$-th energy level for two differentone-dimensional random potentials. This distribution is shown to be related tothe distribution of the distance between two consecutive nodes of the wavefunction.  We first consider the case of a white noise potential and study thedistributions of energy level both in the positive and the negative part of thespectrum. 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 ascaling law which is shown to be related to the extreme value statistics of aset of independent variables.  In the second part we consider the case of a supersymmetric randomHamiltonian (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 thatthe ground state energy, which behaves on average like $\exp{-L^{1/3}}$ inagreement 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 thecase when $\phi(x)$ has a non zero mean value.Comment: LaTeX, 33 pages, 9 figure

Individual energy level distributions for one-dimensional diagonal and off-diagonal disorder