A vector operator ##\mathbf{V}## is defined as one satisfying the following property:(adsbygoogle = window.adsbygoogle || []).push({});

## [V_i,J_j] = i\hbar \epsilon_{ijk}V_k##

where ##\mathbf{J}## is an angular momentum operator. My question is what is the role of ##\mathbf{J}##, does it have to be the total angular momentum from all angular momenta appearing in the system, i.e. if we don't consider spin then ##\mathbf{J}=\mathbf{L}##, if we consider it then ##\mathbf{J} = \mathbf{L}+\mathbf{S}##?

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# Vector Operator

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