(a) Check that Arj₁ (kr) satisfies the radial equation with V(r) = 0 and ℓ = 1.
(b) Determine graphically the allowed energies for the infinite spherical well, when ℓ = 1. Show that for large N, E_N1 ≈ (ћ²π²/2ma²) (N + 1/2)².

First show that j₁ (x) = 0 ⇒ x = tan x. Plot x and tan x on the same graph, and locate the points of intersection.