The basic problem of quantum integrability has been systematically studied
with an algebraic approach. With the introduction of the dynamical symmetry
algebra the difficulty in transferring the classical integrability conditi
on into (quantum mechanics is resolved. Using the superconvergent technique
of Kolmogorov, it has been proved that systems with Hamiltonians expressed
merely with elements of a definite dynamical symmetry algebra form an inte
grable class of systems corresponding to that dynamical symmetry.