How to expand quantum mechanical angular momentum.

[Luyang Han]

Hello all,

I have some question about how to expand the angular momentum into certain
basis. Consider we have some angular momentum state with total angular
momentum l, we can select the basis as |l,mz>, which is the eigenstate of
Lz operator. But equivalently we can also select |l,mx> or |l,my> as the
basis. Then how to transform from one to another?

Or put it simple, how to calculate:
<l,mx|l,my>
<l,my|l,mz>
<l,mz|l,mx>
, where mx, my, mz = -l, -l+1, ...l-1, l

Thanks!!!

Luyang Han