This is a very simple question, but I can't seem to get it right, there's probably something silly that I'm missing here. Here's the question:(adsbygoogle = window.adsbygoogle || []).push({});

I have A system in the l=1 state, and I have L_z|\ket{lm} = \hbar m\ket{lm}and L^2 \ket{lm} = \hbar^2 l(l+1)\ket{lm}

I need to find the eigenvalues and eigenvectors of L_x and L_y using the eigenvectors of L_z and L^2, assuming they are \ket{1,0}, \ket{1,-1} and \ket{1,1}.

I use that L_x = \half (L_{+}+L_{-}) and get this:

L_x(A\ket{1,0}+B\ket{1,1}+C{\ket{1,-1}) = \half \hbar \sqrt{2}( A\ket{1,-1}+A\ket{1,1} + B\ket{1,0} + C\ket{1,0})

Ignoring the \half \hbar \sqrt{2} constant, I equate and get:

A = B, A=C, and B+C=A. Which is obviously wrong... so what am I missing here? I feel like I'm missing a 1/2 or 2 somewhere....

Thanks in advance, this question has been annoying me for ages...

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# Homework Help: Angular Momentum, L_x eigenvalues and eigenfunctions

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