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.
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