(1) When the energy of a system (simple harmonic oscillator) is given by E = heat bath of (constant) temperature T, (a) Calculate the partition function Z. (b) For high temperature kT >> ħw, derive the approximate form of Z. = ( n + 1/2) hw in (c) Calculate F (Helmholtz free energy), U (internal energy), and S (entropy) of the system.

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