(a) Calculate the time-averaged kinetic energy and potential energy of a one-dimensional harmonic oscillator, both classically and quantum-mechanically, and show that the results obtained are consistent with the result established in the preceding problem (n=+2).
(b) Consider, similarly, the case of the hydrogen atom (n=−1) on the basis of (i) the Bohr--Sommerfeld model and (ii) the Schr\"odinger model.
(c) Finally, consider the case of a planet moving in (i) a circular orbit or (ii) an elliptic orbit around the sun.