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I K dot p method with SO interaction

  1. Aug 21, 2016 #1
    I am trying to derive the k dot p formula with the spin orbit interaction term included. I am having some trouble. I insert a bloch wave function multiplied with an unspecified spinor. But how do I treat the cross product term that comes from the SO and what is the effect of the pauli matrix vector on the spinor? And also: Since the spin orbit term contain the gradient of the coulomb potential how can I let p act on the bloch states? (I assume this how you derive the correct formula?)
    The result I want is the attached. Also I attached what I have written up so far.
     

    Attached Files:

  2. jcsd
  3. Aug 26, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
  4. Aug 27, 2016 #3

    DrDu

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    This is a problem of degenerate perturbation theory. I would first try to diagonalize the sigma matrices.
     
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