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Zeeman Effect with a matrix involved

  1. Apr 7, 2013 #1
    Please refer to picture (1). This the equation of motion for an electron in a magnetic field along the z direction and moving with a certain velocity. Where Ω is the Larmor's frequency.
    Then refer to picture (2), that is the matrix representing the previous equation. How was this matrix arranged. I didn't understand a thing.

    Any help is much appreciated.
    Please excuse me for the bad resolution of the images.
     

    Attached Files:

  2. jcsd
  3. Apr 7, 2013 #2
    I think this is done by assuming that each component of r is of the form exp(i*omega*x). Then you put that in the first equation and work out what the equations are for each component and rewrite it in matrix form.
     
  4. Apr 7, 2013 #3
    Yes, that's true, your assumption is written also.. Can you please elaborate more?
     
  5. Apr 8, 2013 #4
    Do you have a more specific question? You should be able to work it out yourself to get the result.
     
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