A Remark on the Transformations between Different Representations

Abstract

The paper respectively studies the transformations of spin component operators and their eigenfunctions from  to  representation. The studies demonstrate that if using the matrix of obtaining from the equation of transforming the eigenfunctions of   and in terms of the transformation arising from Ref. [7] for all of the spin component operators from  to    representation, a negative symbol will occur in the result, which is not concordant with the commutation relation between  and . Moreover, this matrix of transformation can not be applied to the transformation of the eigenfunctions of  or . It therefore concludes that with respect to the transformation of representation of an operator and its eigenfunctions, the matrix of transformation should be obtained from the equation of transforming the eigenfunctions of the same operator from the old to the new representation.