Solve L=2 Atom Problem: Find Min (L_x)^2 + (L_y)^2

[PsychonautQQ]

Homework Statement

For an electron in an atom that is an l=2 state, find the smallest value of (L_x)^2+(L_y)^2.

Homework Equations

The Attempt at a Solution

okay so L = (l(l+2))^(1/2)

and that squared with l =2 would be 6h(bar)^2

kind of running into a wall here..
Or is it the maximum value of (L_x)^2 + (L_y)^2 occurs when (L_z)^2 is a maximum value? and L_z = m_l*h(bar).. which would have a maximum value of 4h_bar^2 so therefore L_x^2 + L_y^2 would be 2h(bar)^2?

Ps I need to learn LaTex X_x

 

[Simon Bridge]

l=2 tells you the Lz state.
How do the Lx and Ly states relate to that?
Hint: conservation of total angular momentum.