(a) Find the chemical potential and the total energy for distinguishable particles in the...

(a) Find the chemical potential and the total energy for distinguishable particles in the three dimensional harmonic oscillator potential (Problem 4.38). Hint: The sums in Equations 5.78 and 5.79 can be evaluated exactly, in this case—no need to use an integral approximation, as we did for the infinite square well. Note that by differentiating the geometric series,

you can get

and similar results for higher derivatives. Answer:

(b) Discuss the limiting case kBT ≪ ħω.

(c) Discuss the classical limit, kBT ≫ ħω, in the light of the equipartition theorem.31 How many degrees of freedom does a particle in the three dimensional harmonic oscillator possess?