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Construct an Operator (2-D QM)

  1. Apr 10, 2009 #1

    Matterwave

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    1. The problem statement, all variables and given/known data
    Construct the [tex]S_r[/tex] operator, which is the spin operator in the r direction.


    2. Relevant equations
    The pauli-matrices are useful, I would assume.

    3. The attempt at a solution
    So, the way we constructed the other 3 operators by noting their effects on a state |s m>

    But I can't do that here because I have no idea what this operator [tex]S_r[/tex] will do to a state |s m>

    I thought about looking at the fact that:

    [tex] x = rsin(\theta)cos(\phi), y = rsin(\theta)cos(\phi), and z=rcos(\theta)[/tex]

    and just replace all the x's with [tex]S_x[/tex]'s and r's with [tex]S_r[/tex]'s etc. But I don't think this will work as it will give me 3 different answers.

    I need help on how to start with this.
     
  2. jcsd
  3. Apr 10, 2009 #2
    If you have a vector A then how do you calculate its component in a certain direction n?

    You take the inner product of the unitvector of the given direction n and the vector A.

    So this is the same case. How would you do it here? ;)
     
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