in a spinorial basis 
jm 
(2j+1 dimensional)
in a spinorial basis jm (2j+1 dimensional)
A 3-d representation of of spinors is a family of cones.
This satisfies:
The cone has an x-y length of 
and a hypoteneuse length of
Relation to 
in coordinate space:
You can represent 
in 
and 
Since 
Then use lowering operator to get other .
For rotation of an wavefunction, 
.
space
Rotations generated by total angular momentum: 
for 
the pauli spin
matrices. This means 
. For electrons 
, 
commute with everything,
so CSCO is 
. This means a general eigenfunction is 
. and 
. 
. rotating
about 
you get 