# Problem in constructing Matrix representation in |↑↓> basis

1. Dec 13, 2011

### ck00

If I want to derive the matrix representation for operator Q in the |S1=1/2 ,m1> |S2=1/2 ,m2 > basis, where |Si,mi> are common eigenstates of S2 , Si,z for the ith particle.

And I do it in this way:
<↑↑|Q|↑↑> <↑↑|Q|↑↓> <↑↓|Q|↓↑> <↑↑|Q|↓↓>
<↑↓|Q|↑↑> <↑↓|Q|↑↓> <↑↓|Q|↓↑> <↑↓|Q|↓↓>
.... .... .... ....
.... .... .... ....

|↑↑>=|S1=1/2 ,m1=+1/2> |S2=1/2 ,m2=+1/2 >
Is it correct?
THANKS

2. Dec 13, 2011

### ck00

can anyone help?

3. Dec 13, 2011

### Fredrik

Staff Emeritus
Let's see...the ij component (row i, column j) in the basis $\{e_i\}$ is $Q_{ij}=(Qe_j)_i=\langle e_i,Qe_j\rangle$. In bra-ket notation, $Q_{ij}=\langle i|Q|j\rangle$. So everything on your first row should have the same "bra", but one of them is different from the other three. I suspect it's just a typo, since the rest of it looks fine.

4. Dec 13, 2011

### ck00

oh,ya, you are right, it's just a typo. Thanks for teaching