Expectation value of angular momentum

[void19]

Homework Statement

Express Lx in terms of the commutator of Ly and Lz , show that <Lx>=0 for this particle.

Relevant Equations

[Ly,Lz]=i(hbar)Lx

⟨Lx⟩=⟨l,m|Lx|l,m⟩=−iℏ⟨l,m|[Ly,Lz]|l,m⟩

 

[PeroK]

You need to show some effort.

 

[Antarres]

Eh, well the formula you wrote under the picture gives exactly the required result, you just have to figure it out. Maybe expand a bit more. Also, $[L_y,L_z] = i\hbar L_x$, so you need to divide by $\hbar$, not multiply. But that doesn't change the result.