I was talking with a guy about energy levels of an atom in a magnetic field. He said that energy levels are shifted and that, if you want know how much, you have to analyze this:
for 1s state:
$$\left<n=1; l=0; m_l=0, m_s', m_i'\ \big|\ a |I \cdot S| + w_0 (L_z+2S_z)\ \big|\ n=1; l=0; m_l=0, m_s, m_i\right>$$
I got curious about the notation, but had to go and I haven't understood very much.. I have knowledge in Analytical Mechanics, but not in Quantum Mechanics. Could you explain me something about the notation employing plain words? Thank you!