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

c = 1

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

\hbar = 1

the Angular momentum:

J^2 \left| l,m \right > = j(j+1) \hbar ^2 \left| l,m\right >

J_z \left|l,m \right> = m \hbar \left|l,m\right>

now becomes :

J^2 \left| l,m \right > = j(j+1) \left| l,m\right >

J_z \left|l,m \right> = m \left|l,m\right>

when we want to calculate the real value, we can recover the \hbar by considering the dimension. the reduced Planck constant has dimension

[\hbar] = [kg][m^2][s^{-1}] = [energy][second]

for example,

E = \omega \hbar