  Three elementary canonical transformations are shown both to have quantum
implementations as finite transformations and to generate, classically and
infinitesimally, the full canonical algebra. A general canonical transformation
can, in principle, be realized quantum mechanically as a product of these
transformations. It is found that the intertwining of two super-Hamiltonians is
equivalent to there being a canonical transformation between them. A
consequence is that the procedure for solving a differential equation can be
viewed as a sequence of elementary canonical transformations trivializing the
super-Hamiltonian associated to the equation. It is proposed that the quantum
integrability of a system is equivalent to the existence of such a sequence.
