[UPSC CSE 2020] Statistical Physics (Q261, 10M)

(i) The energy level of a quantum harmonic oscillator with frequency \nu is given by E_n=\left(n+\frac{1}{2}\right)h\nu,\quad \text{where } n=0,1,2,\ldots Calculate its partition function.

(ii) Calculate the partition function of a two level system.