quantum mechanics - Canonical Commutation Relations in arbitrary Canonical Coordinates

If one were to formulate quantum mechanics in an arbitrary canonical coordinate system, does he impose canonical commutation relations using Dirac's recipe?

$$[\hat{Q}_i,\hat{P}_j]~=~i\hbar~\{q_i,p_j\}$$

Here $q_i$ and $p_j$ are canonical coordinates and conjugate momenta; $\hat{Q}_i$ and $\hat{P}_j$ the respective quantum operators; and $\{\}$ and and $[]$ the Poisson bracket and quantum commutator.

In this recipe, does one define the quantum momentum operators like this?

$$\hat{P}_i~=~-i \hbar \frac{\partial}{\partial q_i}$$

There's a comment on a post below that says this recipe does not always work. Can someone shed more light on this?

Which coordinate system confirms quantum-level experimental data?

Please suggest references on this subject.