A system of N paticles has a Hamiltonian of the form H = -h S (-1 where h is a positive constant. Each particle can have an "spin" S = 1,0,-1. a. In the canonical ensemble find the partition function of the system. b. Find the average energy of the system. c. Find the average number of particles in the state S = 1. d. Using the microcanonical ensemble find an expression for the number of states for which the system has energy E. e. Use your result from part d to check your answer from the canonical ensemble result in part c. (note: part e is hard so attempt only after you are done with the rest of the exam!)