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 functiom. F

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 functiom. F