For any l 0, the effective potential vr( for the hydrogen atom has a local minimum at some finite non-zero value of r. approximating the potential by a parabola in the vicinity of the minimum, for any 1 〉 0 estimate the binding energy by comparison of the radial schrödinger equation with the 1d harmonic oscillator. compare your estimates to the exact answer for the state of lowest energy for a given value of e > 0. (remember that binding energy is measured relative to the energy of completely separated particles, not relative to the minimum value of the potential). note: this sort of approximation is not really needed for the hydrogen atom, since we can work out the orbital energies exactly, but it can be useful to approximate energies in multi-electron atoms.