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QM Spin Function Question

  1. Oct 16, 2013 #1
    1. The problem statement, all variables and given/known data
    A number of spin 1/2 particles are run through a Stern-Gerlach apparatus and when the emerge they all have the same spin wave function (ψ1, ψ2)τ and 9/25 are in the +z direction and 16/25 are in the -z direction with the normal basis column vectors for +z and -z.

    Determine a possible normalized spin wave function
    1, ψ2)τ


    2. Relevant equations



    3. The attempt at a solution


    I am not sure where to start, all i can think of is to have 9/25(+z) = (9/25,0)τ and 16/25(-z) = (0, 16/25)τ to yield a total wave function of (9/25,16/25)τ
    but I don't know what to do for the normalization or if my initial thought was even on the right track? Thanks for the guidance!
     
  2. jcsd
  3. Oct 17, 2013 #2

    fzero

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    You are on the right track, but have confused the relationship between the wavefunction and the probability to find a particle in a given quantum state.

    First, since you are worried about the normalization, if we are given a spin wavefunction ##( \psi_1 ~~\psi_2)^T##, can you express the norm of this vector in terms of ##\psi_{1,2}##?

    Can you use the previous result to derive a normalized wavefunction (call it ##\Psi## for the same superposition of states?

    Now, given ##\Psi## can you express the probability to find the particle in the +z direction in terms of ##\psi_{1,2}##? Think in terms of inner products.

    Do the same for the -z direction.
     
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