Commutation relation for L_3 and phi

[ythaaa]

Hi, just wondering whether the commutation relation $$[\phi,L_3]=i\hbar$$ holds and similar uncertainty relation such as involving X and Px can be derived ?

thanks

 

[malawi_glenn]

testing that commutator is simple, since $$L_z \sim \frac{d}{d\phi}$$, let the commutator act on a function $$F(r,\phi,\theta)$$ and then you\ll have it.

The same thing for [x,P_x]