The total spin operator Ŝ2 operator commutes with all spin free Hamiltonians. Apart from the spatial point group symmetry the spin symmetry is frequently the only useful symmetry of a physical system (this is true in particular for molecular systems). Moreover, the isospin operator T̂ of nucleons has the same formal properties as the total spin operator Ŝ2. Construction and use of the spin eigenfunctions is therefore particularly important and whole monographs are devoted to this subject (cf Pauncz 1979). From the point of view that I have adopted here, namely GRMS, the thing that is important is not how to construct spin eigenfunctions, but how to find proper graphical labels for them. In the second part of this work I will show how the information contained in the labels or in the structure of graphs may be used to calculate arbitrary matrix elements.
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