Natural unit

on Size and Unit, we know that the speed of light better be equal to 1, that simplify the equation of relativity.

now, we impose 1 more things, the Reduced Planck constant, h_bar also set to 1. that simplify all equations with angular momentum or spin.

the Angular momentum:

L^2 | l, m > =  h_bar l ( l+1) |l, m >
Lz |l, m > = h_bar m |l, m >

now becomes :

L^2 | l, m > =   l ( l+1) |l, m >

Lz |l, m > =  m |l, m >

this is same for the spin. 

by doing so, the magnetic moment will be

mu = g x muB x S or g x muB x L

since there is no h_bar in S or L anymore.