As last post discussed, finding to CG coefficient is not as straight forward as text book said by recursion.

However, there are another way around, which is by diagonalization of

first we use the identity:

when we “matrix-lize” the operator. we have 2 choice of basis. one is , which give you non-diagonal matrix by the terms. another one is , which give you a diagonal matrix.

Thus, we have 2 matrixs, and we can diagonalized the non-diagonal. and we have the Unitary transform P, from the 2-j basis to j basis, and that is our CG coefficient.

oh, don’t forget the normalized the Unitary matrix.

i found this one is much easy to compute.

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