Spin Orbit Interaction Hamiltonian

  • Thread starter QMrocks
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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?
 
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  • #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....
 
  • #3
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Dr Transport said:
Messiah, Sakaurai, Cohen-Tannouji, Bjorken & Drell, all of those texts have the spin-orbit interaction defined in them and their derivations....
Thank you!
 
  • #4
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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.
 
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QMfunster said:
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.
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.
 
  • #6
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Yes, I agree. Starting from relativistic quantum theory is definitely the most straightforward way to get to the correct result.
 

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