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Carbon nanotubes

  1. Feb 26, 2013 #1
    Im doing a problem with a simple model of a carbon nanotube. In this we have an electron which is bound to the surface of a cylinder from which there is a radially outpointing electric field.
    We choose to put the x-axis along the axis of the cylinder such that the coordinate describing rotation around the cylinder is directly related to its angular momentum.
    Now I am asked to argue that the expectation value of Lz and Ly are 0 with a physical argument. I am not sure how to approach this. Only thing I can see is that the system is symmetric under rotation around the x-axis, but I don't see where this leads me.
     
  2. jcsd
  3. Feb 26, 2013 #2

    mfb

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    A non-zero Lz or Ly would point in some specific direction, and ruin your symmetry.
     
  4. Feb 26, 2013 #3
    but this isn't exactly as non-zero Lz or Ly it is a non-zero expectation value.. I don't completely understand I must admit - can you elaborate? :)
     
  5. Feb 26, 2013 #4

    mfb

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    I meant a non-zero expectation value in my post. This would break symmetry: You would get a preferred direction (the direction of the spin expectation value) instead of your symmetric setup.
     
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