(a) Construct the wave function for hydrogen in the state n=4, ℓ=3, m=3. Express your answer as a function of the spherical coordinates r, θ, and ϕ.
(b) Find the expectation value of r in this state. (As always, look up any nontrivial integrals.)
(c) If you could somehow measure the observable Lx2+Ly2 on an atom in this state, what value (or values) could you get, and what is the probability of each?