Challenging Quantum Problem

[Galileo]

Yep. The quick way of seeing this intuitively is by recalling that $\vec \nabla V$ is the vector which, at eacht point, points in the direction of maximum increase of V. If V is spherically symmetric, what other direction can this be but radially outward? In the tangential direction it must be zero.
So $\vec \nabla V(r)$ points in the direction of $\vec r$ everywhere, so its cross product with $\vec r$ is zero everywhere.

 

[harsh]

Actually, you could have used the equation is suggested. The commutator [H,L] is zero, and <dl/dt> is obviously zero. Its a nifty little formula, and its very useful.

- harsh