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Homework Statement
Two particles, their spin are 1/2.
The hamiltonian is ##H=\gamma s_1 \cdot s_2##
At t=0, the state ##|\alpha(0)>## is such as ##s_{1z}|\alpha(0)>=\hbar/2 |\alpha(0)>## and ##s_{2z}|\alpha(0)>=\hbar/2 |\alpha(0)>##. Find the state ##|\alpha(0)>##.2. The attempt at a solution
I think that ##|\alpha(0)>=|1,1>## in the base of total angular momentum, i.e. |1/2, 1/2> in the other one. But the correct result seems to be ##|\alpha(0)>=1/ \sqrt2 [|1,1; 1/2, 1/2> + 1/ \sqrt 2 (|1,0; 1/2, 1/2>+|0,0; 1/2, 1/2>)]##.. what's wrong?
I used the following table: