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I understand you can accept the fact that commutators of compatible measurables equal zero, while those of incompatible measurements equal something like -ih. and after accepting these relationships you can derive a lot of other properties of your system.

I have seen explanations of the commutators in quantum mechanics as the quantum-mechanical version of the poisson brackets. But this explanation is not intuitive enough for me. ( I think better in terms of pictures rather than symbols on paper).

I have also read the approach by Sakuray, which almost led me to understand the issue but not quite.

I'll appreciate any insights on this topic.