Answer to Question #145710 in Quantum Mechanics for Viccy

Question

Write down Ly is term linear angular momentum.

Answer 1

In quantum mechanics, the angular momentum operator has a form similar to classical mechanics:

$\hat{L}= \hat{r} \times \hat{p}$

but momentum (or linear momentum) operator in quantum mechanics has a form $\hat{p} = -i \hbar \nabla$.

From the properties of cross product:

$L_y = zp_x−xp_z$

This is the expression of y component of angular momentum in terms of linear momentum components.