2. Quantum harmonic oscillators: consider N independent quantum oscillators subject to a Hamiltonian H (In}) = L hw (n,+;). H ({n,}) =£ħa where n, = 0, 1, 2, .. is the quantum occupation number for the ith oscillator. (a) Calculate the entropy S, as a function of the total energy E. (Hint. N(E) can be regarded as the number of ways of rearranging M =E,n, balls, and N-1 partitions along a line.)

2. Quantum harmonic oscillators: consider N independent quantum oscillators subject to a Hamiltonian H (In}) = L hw (n,+;). H ({n,}) =£ħa where n, = 0, 1, 2, .. is the quantum occupation number for the ith oscillator. (a) Calculate the entropy S, as a function of the total energy E. (Hint. N(E) can be regarded as the number of ways of rearranging M =E,n, balls, and N-1 partitions along a line.)