Finding <Lx²> + <Ly²> for particle in state with l=3, m=+2

[hellosir]

For a particle in the state Y(l=3, m=+2), how do I find <Lx^2> + <Ly^2> ? I'm lost. THanks!

 

[blechman]

1) You can do it by brute force - compute the relevant integrals (I don't advocate this method).

2) Consider the following useful fact:

$$L_x^2+L_y^2=L^2-L_z^2$$