Lx is measured to be h, what is the most likely outcome of the next measurement of Lz
The Attempt at a Solution
So far I built the matrix Lx with |lm> basis where |lm> is a eigenfunction of Lz, for l =1.
Not being not sure where to go from there I went for a more direct method of taking the projection < lz, mz | lx=1, mx=1> and solving it, and the one with the largest magnitude would win. But the only way I could figure that would be to expand < lz, mz | lx=1, mx=1> into < lz, mz | n >< n l lx=1, mx=1>, where n is the directional eigenket, which I believe gives two spherical harmonics where later has to be rotated from x to z.
To sum up I feel pretty insecure about all this and hope there's a better way.