GATE 2020 PH – Question 27
Particle A with angular momentum $j=3/2$ decays into particles B and C of angular momenta $j_1,j_2$. If $$|3/2,3/2\rangle_A=\alpha|1,1\rangle_B\otimes|1/2,1/2\rangle_C,$$ find $\alpha$.
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Correct answer: 1 to 1
Explanation
This is the highest-weight state for addition of angular momenta 1 and 1/2. The maximum projection $M=3/2$ can be formed only by $m_1=1,m_2=1/2$. The normalized coupled state is exactly that product, with Clebsch–Gordan coefficient +1 in the standard phase convention. Thus $\alpha=1$.