Study of spectral statistics of classically integrable systems

In this work we present the results of a study of spectral statistics for a classically integrable system, namely the rectangle billiard. We show that the spectral statistics are indeed Poissonian in the semiclassical limit f or almost all such systems, the exceptions being the atypical rectangles wi th rational squared ratio of its sides, and of course the energy ranges lar ger than L-max = h/T-0, where T-0 is the period of the shortest periodic or bit of the system, however L-max --> infinity when E --> infinity.