Consider the following states of the hydrogen atom corresponding to [itex]l=2[/itex] whose quantum numbers corresponding to [itex]L_z[/itex] and [itex]S_z[/itex] are given by [itex]m_l=2[/itex], [itex]m_s=-1/2[/itex] and [itex]m_l=1[/itex], [itex]m_s=1/2[/itex]. What are the possible values for the quantum number j for the states [itex]m_j=3/2[/itex]?
This is where the problem lies. In my class notes, I noted that [itex]m_j=m_l+m_s[/itex] but for the second cases this makes no sense.
I also have noted [itex]j=l+s, l+s-1,...,|l-s|[/itex].
The Attempt at a Solution
I tried to find some information on j in hyperphysics and wikipedia but I'm still stuck. I don't really understand what is the j. Is it just an index used in the "[itex]m_j[/itex]"? And [itex]m_j[/itex] is the quantum number for the total angular momentum of the atom? I don't really understand what it means.