Introductory Quantum HW (Angular Momentum)

1. The problem statement, all variables and given/known data
Consider a three-dimensional system with wave function ψ. If ψ is in the l = 0 state, we already know that Lzψ=0. Show that Lxψ=0 and Lyψ=0 as well.

2. Relevant equations

[Lx,Ly]ψ = i*h-bar*Lzψ

3. The attempt at a solution

I’m having trouble figuring out where to start this. I think it should be clear and straight-forward, but for some reason I’m just not seeing how I can derive this. I tried using the above equation, to get


I assume from here I would prove that this is only true of Lxψ and Lyψ are 0. That is assuming, I’m on the right track.

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