Irreducible Bases and Correlations of Spin States for Double Point Groups

In terms of the irreducible bases of the groupspace of the octahedral double group O ananalytic formula is obtained to combine the spin states|j, > into the symmetrical adapted basesbelonging to a given row of a given irreducible representationof O. This method is effective for alldouble point groups. However, for the subgroups ofO there is another way to obtain thosecombinations. As an example, the correlations of spin states for thetetrahedral double group T are calculatedexplicitly.