We perform an analysis of a graphical representation for the addition of two angular momenta, focusing our attention on the angle delta between the xy components of two angular momenta. Then we propose a new complete set of commuting observables, which differ from the usual sets that are connected by the Clebsch-Gordan coefficients. This set shows that the angle delta can be a well-defined variable in quantum mechanics. An empirical analysis of the graphical representations of the angular momenta relations, which may include the angle delta, followed by quantum mechanical considerations, leads to the vanishing of certain quantum angular momentum commutators for specific states. Therefore, although the commutators are not null in general, the quantum addition of angular momenta may be represented using classical-like diagrams. (C) 1999 American Association of Physics Teachers. [References: 11]
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