Heisenberg's famous commutator of a pair of conjugated canonical variables is formulated for position and conjugated momentum
$$[q,p] = i\hbar.$$
Intuitively I would guess that it would also work other pairs of conjugated variables, in particular those obtained by canonical transformation from $(q,p)$. However, actually I have never seen a canonical transformation in Quantum Mechanics (well, may be the pair of an annihilation and creation operators are result of canonical transformation ... actually I never checked that). In particular I would be interested if in Quantum Mechanics angle-action variables are used, which can be obtained from the $(q,p)$-pair by a canonical transformation. As the action plays a promiment role in Quantum Mechanics (for instance in the path integral) I would expect the appearance of angle-action variables in Quantum Mechanics, but actually I have never seen it.
What's all about -- are canonical transformations a tool used in QM or is it limited only to classical physics? Are angle-action variables are of interest and use in QM?
