(a) Calculate the time-averaged kinetic energy and potential energy of a one-dimensional harmonic oscillator, both classically and...

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(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 (with \(n=2\) ).

(b) Consider, similarly, the case of the hydrogen atom \((n=-1)\) on the basis of (i) the BohrSommerfeld model and (ii) the Schrödinger model.

(c) Finally, consider the case of a planet moving in (i) a circular orbit or (ii) an elliptic orbit around the sun.

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