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A mathematical construct quantifying the difference in effect of applying two operators in two alternate successions. It is the defining product of a Lie algebra, the efficient underlying description of Lie groups, of use in several areas of physics, most notably quantum field theory.

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Why should not $\hat X$ and $\hat P$ commute in quantum mechanics?

I have heard if we want to obtain classical results from quantum mechanics, we have to choose the commutator of $\hat X$ and $\hat P$ to be $\left[\hat X,\hat P\right]=i\hbar$. …
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