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Matrix representation of a quantum system

  1. Oct 3, 2016 #1
    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]'] MR5aRwH.jpg
    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]'] 7qaYfVU.jpg
     

    Attached Files:

  2. jcsd
  3. Oct 3, 2016 #2

    DrClaude

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    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?
     
  4. Oct 3, 2016 #3
    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|+>
     
  5. Oct 3, 2016 #4

    DrClaude

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    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?
     
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