What Does ee in H_ee Stand For?

[Wminus]

Homework Statement

See uploaded file.

Homework Equations

I guess one needs to keep in mind this:
https://en.wikipedia.org/wiki/Complete_set_of_commuting_observables

The Attempt at a Solution

Basically, my question is about the notation:

1) What does the subscript "ee" stand for in H_ee? And "pq" in r_pq??
2) Why is the hamiltonian bolded like it was a vector in the assignment??
3) What is $H_{LS}$?
4) Are these operators used to describe a many-electron atom?

 

[Wminus]

By the way, don't the spin operator and orbital angular momentum operator act on separate wavefunctions in separate hilbert-spaces? So is it even possible to find the commutation between them?

 

[blue_leaf77]

1) What does the subscript "ee" stand for in H_ee? And "pq" in r_pq??
2) Why is the hamiltonian bolded like it was a vector in the assignment??
3) What is HLSH_{LS}?
4) Are these operators used to describe a many-electron atom?

All these questions except for the second can be found in the discussion preceding the questions that you posted. Where did you find those problems?

 

[Wminus]

All these questions except for the second can be found in the discussion preceding the questions that you posted. Where did you find those problems?

actually there was no discussion preceding it, but no worries I found out about it. The professor told me in class what he meant.