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Please try to include the following

• main points understood, and expand them - what is your understanding of what the points were.
  • expand these points by including many of the details the class discussed.
• main points which are not clear. - describe what you have understood and what the remain questions surrounding the point(s).
  • Other classmates can step in and clarify the points, and expand them.
• How the main points fit with the big picture of QM. Or what is not clear about how today's points fit in in a big picture.
• wonderful tricks which were used in the lecture.
  

Fine structure is due to two mechanisms: relativistic correction and spin-orbit coupling. In other words, a very small perturbation (correction) to the Bohr energies.

The equation of which is: <math>H_{fs}=\alpha\vec{S}\vec{L}</math>

By considering the relativistic version of momentum: <math>p=\frac{mv} {\sqrt{1-(\frac v {c})^2}}</math>. We can derive the relativistic equation for kinetic energy: <math>T=\sqrt{m^2c^4+p^2c^2}-mc^2</math>.

With <math>p«mc</math> (the non-relativistic limit) we get <math>T=\frac {p^2} {2m}-\frac{p^4} {8m^3c^2}</math>

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