# Angular Momentum Commutation Rules

## Theorem

Let $J_x$, $J_y$ and $J_z$ denote the angular momentum operators.

Then:

 $\displaystyle \sqbrk {J_x, J_y}$ $=$ $\displaystyle i J_z$ $\displaystyle \sqbrk {J_y, J_z}$ $=$ $\displaystyle i J_x$ $\displaystyle \sqbrk {J_z, J_x}$ $=$ $\displaystyle i J_y$

where $\sqbrk {\, \cdot, \cdot \,}$ denotes the commutator operator.