We have noted that for a given energy, as ℓ increases, the motion is more like a circle at...

We have noted that for a given energy, as ℓ increases, the motion is more like a circle at a constant radius, with the rotational energy increasing as the radial energy correspondingly decreases. But is the radial kinetic energy 0 for the largest ℓ values? Calculate the ratio of expectation values, radial energy to rotational energy, for the (n, ℓ, mℓ) = (2,1, +1) state. Use the operators

which we deduce from equation (7-30).