In addition, systems which display chaotic classical motion are expected to be characterized by the statistics of random matrix eigenvalue ensembles. For systems invariant under time reversal, the energy-level statistics of a number of chaotic systems have been shown to be in good agreement with the predictions of the Gaussian orthogonal ensemble (GOE) of random matrices, and it has been suggested that this phenomenon is generic for all chaotic systems with this symmetry. If the normalized spacing between two energy levels is s , the normalized distribution of spacings is well approximated by