Matrix representation of a quantum system

[whatisgoingon]

Homework Statement

I have to find the matrix system of S_x, S_y , and S_z using the given information:
190899[/ATTACH]']

Homework Equations

The Attempt at a Solution

for attempting S_x:
Ignoring the ket at the bottom, I would get S_x|+> = +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 S_x equation? Giving me the matrix representation of 190901[/ATTACH]']

 

[DrClaude]

Ignoring the ket at the bottom, I would get Sx|+> = +ħ/2[[0,1],[1,0]]

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?

 

[whatisgoingon]

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.

whoops, I meant S_x is represented as ħ/2 [[0,1],[1,0]].

And how can you obtain that result without considering "the ket at the bottom?

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|+>

 

[DrClaude]

whoops, I meant S_x is represented as ħ/2 [[0,1],[1,0]].

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

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.

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

Also isn't the dirac representation just the bra and ket?

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