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calculate the probability of the harmonic oscillator En = (n + 1/2)hw is a state with n an odd number if the oscillator is in contact with heat bath at temperature T ?

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(1) A single particla quantum mechanical oscillator has energy levels (n + 1/2) hw, where n = 0, 1, 2, .. and w is the natural frequency of the oscillator. This oscillator is in thermal equi- librium with a reservoir at temperature T. (a) Find the ratio of probability of the oscillator being in the first excited state (n = 1) to the probability of being in the ground state. (b) Assuming that only the two states in Part la are occupied, find the average energy as a function of T. (c) Calculate the heat capacity at a constant volume. Does it depend on temperature?
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