7. form A system of N three-level particles has a Hamiltonian of the H Pa -h...

 

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7. form A system of N three-level particles has a Hamiltonian of the H Pa -h N S₁ S₁ = 1, 0. -1 www i=1 where is a positive constant. (This might represent the energy levels of spin-1 particles in an applied magnetic field.) If ng is the average number of particles in the state S (S = 1, 0, -1), use the microcanonical ensemble to find the ratio / in terms of the temperature in the limit N →∞. Hence find the Helmholtz free energy F(T, N). Check your answer for F(T, N) by using the canonical ensemble (which is much easier). Identify the limits in which the information on the state of the system is maximum and minimum and find the entropy in these cases. 7. form A system of N three-level particles has a Hamiltonian of the H Pa -h N S₁ S₁ = 1, 0. -1 www i=1 where is a positive constant. (This might represent the energy levels of spin-1 particles in an applied magnetic field.) If ng is the average number of particles in the state S (S = 1, 0, -1), use the microcanonical ensemble to find the ratio / in terms of the temperature in the limit N →∞. Hence find the Helmholtz free energy F(T, N). Check your answer for F(T, N) by using the canonical ensemble (which is much easier). Identify the limits in which the information on the state of the system is maximum and minimum and find the entropy in these cases.