Prove Lk and r^2 Commutator = 0

[jc09]

Homework Statement

Show that [ Lk , r^2] = 0

Homework Equations

The Attempt at a Solution

know that L=r x p=r x(-ih(bar)V)

 

[Cyosis]

With the k I take it you mean the third component?

Lets write it like this [Lz,r^2]=[Lz,x^2+y^2+z^2]=[Lz,x^2]+[Lz,y^2]+[Lz,z^2]. Can you work out these three commutators?