Problem 3 A simple model for a classical one-dimensional solid consists of M independent oscillators, each with energy 2 1 e(z,p) = 2pm + Emw2x2 where w is the angular frequency. (a) Write the partition function for a single oscillator. (Hint: [ e%"dy = V) (b) Write the partition function for a system of M oscillators. (c) Compute the Helmholtz free energy for this system. ) (d) Compute the entropy for this system