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    Energy as function of temperature for Einstein solid

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    As per the attachment, I understand what formula needs to be used, but I am unsure of what to do from this point.

    See attached file for full problem description.

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    Solution Preview

    I'll explain the derivation from the beginning for the microcanonical ensemble.

    The number of oscillators is three ties the number of atoms. Let's denote the number of oscillators as N. If we measure the energy relative to the zero point energy of 1/2 h-bar omega N, then the total energy is:

    n_1 + n_2 + n_3 +...+ n_N = U (1)

    where the n_j are the quantum numbers of the oscillators and U is the energy E divided by h-bar omega:

    U = E/(h-bar omega) (2)

    The multiplicity of a macrostate containing energy E follows by calculating how many solutions Eq, (1) has for fixed U. You can again translate this to an ...

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