New Conserved Quantities and Test for Regular Spectra

When Einstein-Brillouin-Keller quantization is possible, it applies to all conserved dynamical variables (not only to the Hamiltonian) and in particular to the time average of any dynamical variable. Thus, for an integrable system of $n$ degrees of freedom, the eigenvalues of $n$ independent constants of motion form a locally regular $n$-dimensional lattice, in the limit $h\to 0$. Failure of doing that may be an indication of quantum chaos.