3.1.2 Angular momentum in an arbitrary direction

1

What is the name for the eigenfunctions of $z$ and square angular momentum?

2

What is their square angular momentum? Their angular momentum in the $z$-direction?

3

What are the names for the quantum numbers of square and $z$ angular momentum?

4

Possible or not? $l=0,m=0$? $l=0,m=1$? $l=1,m=0$? $l=1,m=1$? $l=1,m=2$? $l=1,m=-1$? $l=2,m=1$? $l=-2,m=-1$?

5

If the angular momentum of a particle is zero, then how does its wave function vary with $\theta$ and $\phi$?

6

The spherical harmonics are messy functions, but the $r^lY_l^m$ are much simpler. What general shape to they take?