Exercise 54 calculates the three oscillator distributions' E = 0 values in the special...

Exercise 54 calculates the three oscillator distributions' E = 0 values in the special case where kBT is ξ. Using a very common approximation technique, show that in the more general low-temperature limit, kBT « ξ, the occupation numbers become ξ/kBT, and 1, for the distinguishable, boson, and fermion eases, respectively. Comment on these results. (Note: Although we assume that kBT « Nω0/(2s + 1), we also still assume that levels are closely spaced—that is, kBT » ω0)