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Classical harmonic oscillator A single classical harmonic oscillator, Kq² 2 with angular frequency w = √K/m is in thermal contact with a heat bath at temperature T. (a) Calculate its canonical partition function, p² 2m H(p, q) = (d) (1) Q(3) = ½ dp dq exp{-BH(p, q)}, (b) Obtain the average (E) of the energy, the variance ((8E)2) of the energy, the free energy A(T), the entropy S(T) and the heat capacity C(T). (c) 2 Compare your results with what you would expect from the equipartition theorem. (2) Consider now that you have 3N classical harmonic oscillators, each one of them with the same angular frequency w, which do not interact with each other. Find the canonical partition function Q(3, N), the average (E) of the energy, the variance ((8E)2) of the energy, the free energy A(T, N), the entropy S(T, N) and the heat capacity C(T, N).

Classical harmonic oscillator A single classical harmonic oscillator, Kq² 2 with angular frequency w = √K/m is in thermal contact with a heat bath at temperature T. (a) Calculate its canonical partition function, p² 2m H(p, q) = (d) (1) Q(3) = ½ dp dq exp{-BH(p, q)}, (b) Obtain the average (E) of the energy, the variance ((8E)2) of the energy, the free energy A(T), the entropy S(T) and the heat capacity C(T). (c) 2 Compare your results with what you would expect from the equipartition theorem. (2) Consider now that you have 3N classical harmonic oscillators, each one of them with the same angular frequency w, which do not interact with each other. Find the canonical partition function Q(3, N), the average (E) of the energy, the variance ((8E)2) of the energy, the free energy A(T, N), the entropy S(T, N) and the heat capacity C(T, N).

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. Classical harmonic oscillator A single classical harmonic oscillator, p² 2m 2 with angular frequency w = √K/m is in thermal contact with a heat bath at temperature T. (a) Calculate its canonical partition function, H(p, q): = Q(³) = 1/2 Kq² + 1/2 dp dq exp{-BH(p, q)}, (1) (2) (b) Obtain the average (E) of the energy, the variance ((SE)2) of the energy, the free energy A(T), the entropy S(T) and the heat capacity C(T). (c) Compare your results with what you would expect from the equipartition theorem. (d) Consider now that you have 3N classical harmonic oscillators, each one of them with the same angular frequency w, which do not interact with each other. Find the canonical partition function Q(3, N), the average (E) of the energy, the variance ((8E)2) of the energy, the free energy A(T, N), the entropy S(T, N) and the heat capacity C(T, N).
Transcribed Image Text:. Classical harmonic oscillator A single classical harmonic oscillator, p² 2m 2 with angular frequency w = √K/m is in thermal contact with a heat bath at temperature T. (a) Calculate its canonical partition function, H(p, q): = Q(³) = 1/2 Kq² + 1/2 dp dq exp{-BH(p, q)}, (1) (2) (b) Obtain the average (E) of the energy, the variance ((SE)2) of the energy, the free energy A(T), the entropy S(T) and the heat capacity C(T). (c) Compare your results with what you would expect from the equipartition theorem. (d) Consider now that you have 3N classical harmonic oscillators, each one of them with the same angular frequency w, which do not interact with each other. Find the canonical partition function Q(3, N), the average (E) of the energy, the variance ((8E)2) of the energy, the free energy A(T, N), the entropy S(T, N) and the heat capacity C(T, N).
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