Exercise 52 gives the Boltzmann distribution for the special case of simple harmonic oscil...

Exercise 52 gives the Boltzmann distribution for the special case of simple harmonic oscillators, expressed in terms of the constant ξ ≡ Nω0/(2s + 1), and Exercise 53 gives the two quantum distributions in that case. Show that both quantum distributions converge to the Boltzmann in the limit kRT » ξ.