  The quantum mechanical version of the four kinds of classical canonical
transformations is investigated by using non-hermitian operator techniques. To
help understand the usefulness of this appoach the eigenvalue problem of a
harmonic oscillator is solved in two different types of canonical
transformations. The quantum form of the classical Hamiton-Jacobi theory is
also employed to solve time dependent Schr\"odinger wave equations, showing
that when one uses the classical action as a generating function of the quantum
canonical transformation of time evolutions of state vectors, the corresponding
propagator can easily be obtained.
