I am trying to find the fermi energy and density of states. From the equation:
what is the big N here?
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Your first equation is $k_F$ in the Sommerfeld model, so long as the variable $n$ is the electron density, $n = N/V$, where $V$ is the volume of the system and $N$ is the total number of electons in the system. I'm not quite sure what you meant to write for $n$, but it probably works out to the electron density.