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Show that the partition function for a simple harmonic oscillator is
e-Bwħ/2
1-e-Bhw
(a) Calculate the internal energy, U and show that the high-temperature result is consistent with the equipar-
tition theorem result.
(b) Calculate the heat capacity, Cy and show that the high-temperature result is consistent with the equipar-
tition theorem result.
(c) Calculate the Helmholtz function, F

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