Abstract
Let \(\hat{\boldsymbol{J}}_{1}\) and \(\hat{\boldsymbol{J}}_{2}\) be two angular momentum operators commuting with each other. Then the basis \(\vert j_{1},m_{1};j_{2},m_{2}>\) of common eigenstates of the operators \(\hat{\boldsymbol{J}}_{1}^{2}\), \(\hat{J}_{1z}\), \(\hat{\boldsymbol{J}}_{2}^{2}\), \(\hat{J}_{2z}\) exists. On the other hand, the total angular momentum \(\hat{\boldsymbol{J}} =\hat{\boldsymbol{ J}}_{1} +\hat{\boldsymbol{ J}}_{2}\) is also an angular momentum operator.
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Grozin, A. (2014). Adding Angular Momenta in Quantum Mechanics. In: Introduction to Mathematica® for Physicists. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-00894-3_18
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