# 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

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

## Angular momentum operator

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

## Imaginary unit

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

## Planck constant

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

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