Given the assumption that the energy levels of an harmonic oscillator can take on only the values

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Given the assumption that the energy levels of an harmonic oscillator can take on only the values \(n h v\) and given the Maxwell-Boltzmann distribution of occupation numbers, show that the probability distribution \(P(n)\) of occupation number \(n\) being realized is a Bose-Einstein distribution and derive the mean occupation number \(\bar{n}\).

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