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In classical mechanics we can easily transform observables fro cartesian to spherical polar coordinate, but in QM it seems difficult(at least for me),for example for r=sqrt(x^2+y^2+z^2), it involves square root of operators;also,I have trouble evaluating relevant commutation relations.

Well I asked this question because I remember calculating <r> in wave mechanics, but we never introduce this kind of operator in formalism.