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I have 2 particles, their spins are s1=3/2 and s2=1/2.

At t=0, the system is described by |a(0)>=|3/2, 1/2, 1/2, 1/2>

I have to find |a(t)>.

I have thought to proceed in the following way:

1) use the basis |s, s_z> where s=s1+s2 and s_z= s_1z+s_2z and find the expressions of these vectors in function of the "old" basis (old basis: |s1, s_1z, s_2, s_2z> )

2) find the expression of |a(0)> in this new basis and then find its expression in function of t.

But something went wrong... For example, if i want to find |s=2, s_z=1>, I have:

|s=2, s_z=1>=a1 |3/2, 3/2, 1/2, -1/2>+a2 |3/2, 1/2, 1/2, 1/2>

If I apply the operator J_, I obtain

[tex]0= \sqrt 3 a_1 |3/2, 1/2, 1/2, -1/2>+ 2 a_2 |3/2, -1/2, 1/2, 1/2>+a_2 |3/2, 1/2, 1/2, -1/2>[/tex].. is it wrong?

And now, how can I find a1 and a2 (normalized)?