For a particular energy level in hydrogen, with quantum numbers n and l, one will find when considering the spin-orbit interaction, the level is split into two fine structure levels with energy separation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\Delta E_{s.o.}=\beta_{nl}(l+1/2)[/tex]

I was trying to prove this result. The spin of an electron is 1/2. Therefore there are two possible values for the total angular momentum, as the spin can be either +-1/2. Therefore using (and the relevant energy spin-orbit equation):

[tex]\Delta E_{s.o.}=E_{j=l+1/2}-E_{j=l-1/2}[/tex]

gives the first result. However, when you follow the proof through I am confused because in the energy spin-orbit equation (not stated here) you use s=1/2 for both possible energy states. However you use l=+-1/2 for the angular momentum. Why is this? Surely you'd use s=+-1/2 for the electron spin also?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Hydrogen spin-orbit interaction

**Physics Forums | Science Articles, Homework Help, Discussion**