# Matrix representation of a quantum system

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1. Oct 3, 2016

### whatisgoingon

1. The problem statement, all variables and given/known data
I have to find the matrix system of Sx, Sy , and Sz using the given information:
190899[/ATTACH]']
2. Relevant equations

3. The attempt at a solution
for attempting Sx:
Ignoring the ket at the bottom, I would get Sx|+> = +ħ/2[[0,1],[1,0]]
but my question here is, does the ket at the bottom(the |±>x = 1/√2 [|+> ± |->] affect the matrix?
because the matrix form of the ket will be 1/√2([1,1]).
With that said, would I have to insert that into the Sx equation? Giving me the matrix representation of 190901[/ATTACH]']

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2. Oct 3, 2016

### Staff: Mentor

That doesn't make sense. The result of an operator on a ket is a ket, so it can be represented as a vector, not a matrix. And how can you obtain that result without considering "the ket at the bottom?"

What is the Dirac representation of a matrix element?

3. Oct 3, 2016

### whatisgoingon

whoops, I meant Sx is represented as ħ/2 [[0,1],[1,0]].
I was under the assumption that the ket |+> = [1,0] and that the ket at the bottom didn't affect it. From your response I guess, it does affect it.

Also isn't the dirac representation just the bra and ket? <+|A|+>

4. Oct 3, 2016

### Staff: Mentor

Ok. But, still, how did you get that matrix?

You have to distinguish between $| \pm \rangle$ and $| \pm \rangle_x$

Yes. What is a single matrix element of the representation of an operator in bracket notation?