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!s_1= 1/2, m_1 =1/2 ; s_2= 1/2, m_2 =1/2 > = !+ + >

!s_1= 1/2, m_1 =1/2 ; s_2= 1/2, m_2 =-1/2 > = !+ - >

!s_1= 1/2, m_1 =-1/2 ; s_2= 1/2, m_2 =1/2 > = !- + >

!s_1= 1/2, m_1 =-1/2 ; s_2= 1/2, m_2 =-1/2 > = !- - >

We have

¦s=1,m_z=1>= ¦++>

¦s=1,m_z=0>= 1/sqrt(2) (¦+->+¦-+>)

¦s=1,m_z=-1>= ¦++>

¦s=0,m_z=0>= 1/sqrt(2) (¦+->-¦-+>)

I understand the spin-1 triplet. My question is "how do you compute ¦+->-¦-+> to get composite s=0,m=0". Is it essentially

1/sqrt(2) (¦1 0> - ¦1 0> )= ¦0 0>

?

Thanks.