3.1.1 Definition of angular momentum

1

Sketch a spherical coordinate system that has a Cartesian z-axis as its axis. Show $r$, $\theta$, and $\phi$.

2

In spherical coordinates, what is the operator of angular momentum in the $z$-direction?

3

Compare this with the operator for linear momentum in the $z$-direction. Does the comparison make sense?

4

What is the form of the eigenfunctions of the angular momentum operator in the $z$-direction?

5

If the angular momentum of a system in a chosen $z$-direction is measured, can it be 3.141593 $\hbar$? If not, why not? What is the closest to that value it could ever come?