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Question: problem 2 5 points the equipartition theorem is valid only...

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PROBLEM 2 5 points] The Equipartition theorem is valid only in classical mechanics and therefore only at height temperatures. One of the very first successes of quantum mechanics was the explanation for why and how exactly the specific heat goes down at low temperatures. In quantum statistical mechanics, the canonical partition function takes the generic form with n the energy eigenstate label and j(n) the degeneracy of that eigenstate, i.e., the number of states with identical energy if we choose not to label them independently. For a single harmonic oscillator n 0,1,2, . . and no degeneracies, j(n)-1. Review this for yourself from your QM course in particular how the frequency w relates the m and K [2] Calculate the partition function and the Helmholtz Free energy for the single harmonic oscillator. This involves a geometric series. a. b. 1 Calculate the internal energy of the harmonic oscillator as an expectation value c. [1] Evaluate the specific heat.

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