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1. The problem statement, all variables and given/known data

Let [tex] U = \text{e}^{i G_3 \alpha} \text{e}^{i G_2 \beta} \text{e}^{i G_3 \gamma}[/tex], where [tex] ( \alpha , \beta , \gamma ) [/tex] are the Eulerian angles. In order that [tex] U [/tex] represent a rotation [tex] ( \alpha , \beta , \gamma ) [/tex], what are the commutation rules satisfied by [tex] G_k [/tex]? Relate [tex] \mathbf{G} [/tex] to the angular momentum operators.

2. Relevant equations

3. The attempt at a solution

I don't really know how to start here. In chapter 3.3 they represent rotation with Euler angles by 2x2 matrices but I don't think that's what I'm supposed to use. Instead I would guess that if [tex] U [/tex] is supposed to be a rotation operator then it has to be an element of either SO(3) or SU(3). Then from the fact that it belongs to one of these groups, one would hopefully get the desired commutation relations.

Any thoughts?

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# Homework Help: Sakurai Ch.3 Pr.6

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