Classical and quantum integrability of Hamiltonians without scattering states

We establish that every quantum Hamiltonian without scattering states has a complete family of conserved quantities independently of the dimension of the system. This result leads to a comparison of the general properties of classical and quantum integrable systems. We discuss several relevant examples and an application to the statistical distribution of energies. As a spin-off, we obtain additional support for the Berry–Tabor conjecture without taking the semiclassical limit into account.