Calculate the following expectation values for the hydrogen atom:
(a) ⟨nl∣r2∣nl⟩,
(b) ⟨nl∣r∣nl⟩,
(c) ⟨nl∣r−1∣nl⟩,
(d) ⟨nl∣r−2∣nl⟩,
(e) ⟨nl∣r−3∣nl⟩,
(f) ⟨nlm∣δ(3)(x)∣nlm⟩.
Note concerning (a–e): Consider the recursion formula proven in the preceding exercise. You then need only compute one expectation value directly.