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## Homework Statement

Suppose in a container there are two spin-1 objects, A and B. It is found that ##J=j_1+j_22## and ##M=m_1+m_2=1##. What is the probability when ##J_z## is measured for A, values of m=0, m=-1 and m=+1 will be obtained?

## Homework Equations

## The Attempt at a Solution

[tex]|j,j> = |2,2> = |(1,1)_A>|(1,1)_B>[/tex]

Starting:

[tex]J_{-}|2,2> = \left(J_{-}^A + J_{-}^B\right)|(1,1)_A>|(1,1)_B>[/tex]

[tex]\sqrt{2(2+1)-2(2-1)}|2,1> = \sqrt{1(1+1)-1(1-1)}\left(|(1,0)_A>|(1,1)_B> + |(1,1)_A>|(1,0)_B>\right)[/tex]

[tex]|2,1> = \frac{1}{\sqrt{2}}\left(|(1,0)_A>|(1,1)_B> + |(1,1)_A>|(1,0)_B>\right)[/tex]

For m=0, probability = 1/2

For m=1, probability = 1/2

For m=-1, probability = 0

Is this right?