# Show that the Hamiltonian operator commutes with the angular momentum operator [closed]

Show that the Hamiltonian operator $\hat{H}= (\hat{p}^2/2m)+\hat{V}$ commutes with all three components of $\vec{L}$, provided that $V$ depends only on $r$. (Thus $H$,$L^2$, $L_z$ are mutually compatible observables). ($\vec{L}$ is $\langle L_x, L_y, L_z\rangle$.)

-

## closed as off-topic by DavePhD, Brandon Enright, John Rennie, JamalS, DanuJun 1 at 8:36

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – DavePhD, Brandon Enright, John Rennie, JamalS, Danu
If this question can be reworded to fit the rules in the help center, please edit the question.

Show that $L_x$ commutes with $(x^2+y^2+z^2)$ and use it to prove it commutes with $r$. Then it follows that $L_x$ commutes with any function of $r$ or $1/r$ and therefore with $V(r)$. Then show that $L_x$ commutes with $(p_x^2+p_y^2+p_z^2)$. So $L_x$ commutes with $H$. $L_y$ and $L_z$ follow by symmetry.