Spin Orbit Interaction Hamiltonian

[QMrocks]

Spin Orbit Interaction Hamiltonian is defined as follows:

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

How does one derive the above Spin Orbit Interaction Hamiltonian from relativistic treatment? Is there a good textbook that elaborates on this?

 

[Dr Transport]

Messiah, Sakaurai, Cohen-Tannouji, Bjorken & Drell, all of those texts have the spin-orbit interaction defined in them and their derivations...

 

[QMrocks]

Messiah, Sakaurai, Cohen-Tannouji, Bjorken & Drell, all of those texts have the spin-orbit interaction defined in them and their derivations...

Thank you!

 

[QMfunster]

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.

 

[QMrocks]

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.

 

[QMfunster]

Yes, I agree. Starting from relativistic quantum theory is definitely the most straightforward way to get to the correct result.