i am now reading the book by woodgate: elementary atomic strucure, 2nd edition.(adsbygoogle = window.adsbygoogle || []).push({});

on page 62, he discusses the spin-orbit coupling in hydrogen atom, and calculates the first order shift of the energy due to this effect.

I have some doubt about his procedure from eq.4.25 to eq.4.27

the spin-orbit coupling is f(r) s \dot l

its average is then <f(r) s\dot l>

why can he take the equality <f(r) s \dot l>= <f(r)> <s \dot l> ?

this greatly simplifes the calculation!

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# About the spin-orbit coupling in atoms

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