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Basic Probability question for a spin 1/2 Particle

  1. Oct 18, 2013 #1
    1. The problem statement, all variables and given/known data

    A beam of spin-1/2 particles is prepared in the state

    [tex]\left|\psi\right\rangle=\frac{2}{\sqrt{13}}\left|+\right\rangle_x+i \frac{2}{\sqrt{13}}\left|-\right\rangle_x[/tex]

    a) What are the possible results of a measurement of the spin component Sz, and with what probabilities would they occur?

    b) What are the possible results of a measurement of the spin component Sx, and with what probabilities would they occur?

    2. Relevant equations

    [tex]P_x=\left|\left\langle x\right| \left. \psi \right\rangle\right|^2[/tex]

    3. The attempt at a solution

    So I can find out the answer to part b just by plugging it straight into the formula and using that [itex]_x\left\langle +\right| \left. + \right\rangle_x=1[/itex] and [itex]_x\left\langle +\right| \left. - \right\rangle_x=0[/itex]

    my problem is with the first part of the question. If I use the same method as before I end up with
    [tex]_z\left\langle +\right| \left. + \right\rangle_x\\
    _z\left\langle +\right| \left. - \right\rangle_x\\
    _z\left\langle -\right| \left. + \right\rangle_x\\
    _z\left\langle -\right| \left. - \right\rangle_x[/tex] in my equations. And I do not understand how to know what these are.
     
  2. jcsd
  3. Oct 18, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    You can express ##_z\left\langle +\right |## in terms of ##_x\left\langle +\right |## and ##_x\left\langle -\right |## (or vice versa).

    Your wavefunction does not look properly normalized.
     
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