(1) A single particla quantum mechanical oscillator has energy levels (n + 1/2) hw, where n = 0, 1, 2, ... and 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?
(1) A single particla quantum mechanical oscillator has energy levels (n + 1/2) hw, where n = 0, 1, 2, ... and 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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Transcribed Image Text:(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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