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Angular momentum

  1. Dec 17, 2007 #1
    1. The problem statement, all variables and given/known data
    Lx is measured to be h, what is the most likely outcome of the next measurement of Lz


    2. Relevant equations



    3. The attempt at a solution
    So far I built the matrix Lx with |lm> basis where |lm> is a eigenfunction of Lz, for l =1.

    Not being not sure where to go from there I went for a more direct method of taking the projection < lz, mz | lx=1, mx=1> and solving it, and the one with the largest magnitude would win. But the only way I could figure that would be to expand < lz, mz | lx=1, mx=1> into < lz, mz | n >< n l lx=1, mx=1>, where n is the directional eigenket, which I believe gives two spherical harmonics where later has to be rotated from x to z.

    To sum up I feel pretty insecure about all this and hope there's a better way.
     
  2. jcsd
  3. Dec 18, 2007 #2
    Ok I figured it out. Solving for the eigenvalues/eigenstates for Lx in a |lm> basis was all I had to do. I wonder how it would compare to that other method.
     
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