Quantum Mechanics: Concepts and Applications · Problem 3.3

Orbital angular momentum in quantum mechanics comes from promoting the classical definition $\vec{L} = \vec{r} \times \vec{p}$ into an operator by replacing position and momentum with their quantum counterparts. The key insight is that $\vec{r}$ becomes the position operator and $\vec{p}$ becomes $-i\hbar\nabla$, so you're really just substituting these operators into the cross product and simplifying the result using commutation relations.

Orbital angular momentum in quantum mechanics comes from promoting the classical definition $\vec{L} = \vec{r} \times \vec{p}$ into an operator by replacing position and momentum with their quantum counterparts. The key insight is that $\vec{r}$ becomes the position operator and $\vec{p}$ becomes $-i\hbar\nabla$, so you're really just substituting these operators into the cross product and simplifying the result using commutation relations.