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Probability that a measurement of Sx will yield hbar for this state

  1. Oct 10, 2012 #1
    1. The problem statement, all variables and given/known data

    Alright, so there is a problem in the Townsend quantum mechanics book that reads: What is the probability that a measurement of Sx will yield the value hbar for this state:


    The state is given by:
    |ψ> = 1/sqrt(14) * (1,2,3i)
    (But the vector is represented as a column vector in state ψ)

    It's in the Sz basis, and it is a spin 1 particle.

    2. Relevant equations



    3. The attempt at a solution

    In another problem I determined the eigenstates of Sx for a spin 1 particle in terms of the eigenstates for |1,1>, |1,0>, |1,-1>. So I figured it would be easy to take that vector for hbar and just do the probability amplitude on it with the given ψ. That vector I have is:

    (1, sqrt(2), 1)

    Again as a column vector. Or row vector, either way really. But when I did that I got a value bigger than 1. So I'm obviously missing something here, and I was hoping someone could tell me what.

    Also I have a huge issue when bases switch, and yes, it's just a lin alg thing and I should review it, but as I do, does anyone have a quick trick for these kinds of problems? It's really appreciated.
     
    Last edited by a moderator: Oct 10, 2012
  2. jcsd
  3. Oct 10, 2012 #2

    vela

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    Hint: Check the normalization of the Lx eigenstate you used.
     
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