1. Consider a system of N independent identical localized particles on a lattice at temperature T (one particle per lattice site). Each particle has energy eigenvalues En = nA, with degener- acy In = n+1, n=0,1,2, 3, ... 20. Here A is a positive constant with the dimension of energy. a) Show that the single-particle canonical partition function z is given by z = [1 e-4/(KT)]=2. b) Calculate the chemical potential for this N-particle system in terms of z