Berry–Tabor conjecture on level statistics of integrable systems

The quantum mechanical system is desymmetrized with respect to all its unitary symmetries, eigenvalues are considered on the scale of the mean level spacing, and generic degeneracies are absent. Let the corresponding classical system be integrable. Berry–Tabor conjecture. The eigenvalues behave like independent random variables, and the distribution of nearest-neighbor spacings is close to the Poisson distribution; in particular, there is no level repulsion. This is one of the standard predictions for quantum-chaotic level statistics, although the paper notes known exceptions such as the harmonic oscillator.