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Spin Orbit Interaction Hamiltonian

  1. Dec 21, 2005 #1
    Spin Orbit Interaction Hamiltonian is defined as follows:

    [itex]
    H_{SO}=\frac{1}{2m_{e}c^2}\frac{1}{r} \left(\frac{\partial V}{\partial r}\right)L\cdot S
    [/itex]

    How does one derive the above Spin Orbit Interaction Hamiltonian from relativistic treatment? Is there a good textbook that elaborates on this?
     
    Last edited: Dec 21, 2005
  2. jcsd
  3. Dec 21, 2005 #2

    Dr Transport

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    Messiah, Sakaurai, Cohen-Tannouji, Bjorken & Drell, all of those texts have the spin-orbit interaction defined in them and their derivations....
     
  4. Dec 22, 2005 #3
    Thank you!
     
  5. Dec 25, 2005 #4
    Thomas precession

    It might be worth mentioning that the "simple derivation" presented in most or perhaps all of those textbooks obtains a final result that is in error by approximately a factor of two. To get the right answer, it is important to carry out a relativistic analysis of what is often called the "Thomas precession" effect. This is addressed at some length in Jackson's textbook on E&M, in Chapter 11 or 12, I believe.
     
  6. Dec 25, 2005 #5
    if we began from Dirac equation, we can obtain the Hamiltonian just like the form in Jackson book. i find L. I. Schiff's book extremely well explained.
     
  7. Dec 25, 2005 #6
    Yes, I agree. Starting from relativistic quantum theory is definitely the most straightforward way to get to the correct result.
     
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