Addition of spin angular momenta
Consider the addition of two spin -1/2 angular momenta, S(1) and S(2)
1. How many states are there in the product basis?
2. If J = S(1) + S(2), what are the possible eigenvalues of the dot product of J and J?
3. By using the recursive algorithm construct all the Clebsch-Gordan coefficients for this problem.
See attached file for full problem description.
This solution provides step by step calculations for states, eigenvalues, and Clebsch-Gordan coefficients.