(a) Construct the spatial wave function (ψ) for hydrogen in the state n=3, ℓ=2, m=1. Express your answer as a function of r, θ, ϕ, and a (the Bohr radius) only—no other variables (ρ, z, etc.) or functions (Y, v, etc.), or constants (A, c0, etc.), or derivatives, allowed (π is okay, and e, and 2, etc.).
(b) Check that this wave function is properly normalized, by carrying out the appropriate integrals over r, θ, and ϕ.
(c) Find the expectation value of rs in this state. For what range of s (positive and negative) is the result finite?