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I'm not altogether sure what you are asking, but I suspect the following may help. To represent rotations, spins and vectors in $SU(2)$ we work as follows. Rotations live in $SU(2)$. Vectors (in the physicist's sense) live in the algebra $\mathfrak{su}(2)$. The position vector $(x,\,y,z)$ is: $$X =x\,\hat{s}_x+y\,\hat{s}_y+z\,\hat{s}_z = ...


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The previous answer is completely right but I want to add some historical comments, since from a historical point of view they have clearly different origins. The Correspondence Principle used to be one of the two fundamental principles of Bohr's theory (one of the main formulations of quantum theory between 1913 and 1923). Originally this principle didn't ...



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