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 €, = acy gn = n+1, n = 0,1, 2, 3, ... o. Here A is a positive constant with the dimension of a) Show that the single-particle canonical partition function z is given by z = b) Calculate the chemical potential for this N-particle system in terms of z. nA, with degener- energy. [1-e-A/(kT)]-2,

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 €, = acy gn = n+1, n = 0,1, 2, 3, ... o. Here A is a positive constant with the dimension of a) Show that the single-particle canonical partition function z is given by z = b) Calculate the chemical potential for this N-particle system in terms of z. nA, with degener- energy. [1-e-A/(kT)]-2,