Berry's Poisson distribution conjecture for integrable quantum systems

Let $H$ be a quantum Hamiltonian whose classical counterpart is integrable, and consider the point spectrum of $H$ (or its normalized energy differences). Berry's conjecture. The point spectrum of a generic quantum system whose Hamiltonian yields a classically integrable system is Poisson distributed; equivalently, the statistical distribution of the differences of normalized energies is generically Poissonian. This conjecture describes the expected spectral statistics of quantum systems associated with integrable classical dynamics and is part of the broader study of statistical distributions of Hamiltonians with pure point spectrum. The source provides no resolution status.