Chapter 11.3, Problem 11.15P

(a)

To determine

Whether the derivation for the commutation relation $\left[L^2,\left[L^2,r\right]\right]=2{\hslash }^2\left(r{L}^2+L^{2}r\right)$.

(b)

To determine

The implications obtained by sandwich the commutator, $\left[L^2,\left[L^2,r\right]\right]$, between $\langle n\text{'}l\text{'}m\text{'}|$ and $|nlm\rangle$.