Formula Angular momentum commutator (Lx and Ly)

Commutator

This commutator for angular momentum is the term you get (in this case: $$\mathrm{i} \, \hbar \, L_{\text z}$$) when you swap the two angular momentum components $$L_{\text x}$$ and $$L_{\text y}$$. As you can see, the commutator is NOT zero.

Angular momentum operator

This is the $$x$$-th component of the angular momentum vector operator $$\boldsymbol{L}$$.

Angular momentum operator

This is the $$y$$-th component of the angular momentum vector operator $$\boldsymbol{L}$$.

Imaginary unit

Imaginary unit is a complex number for which is true: $$\mathrm{i} ~=~ \sqrt{-1}$$.

Planck constant

Planck constant is a natural constant (of quantum mechanics) and has the value: $$\hbar ~=~ \frac{h}{2\pi} ~=~ 1.054 \cdot 10^{-34} \, \text{Js}$$