= Solution
Use the quantum <free electron model>: conduction <Electrons> move as independent particles in a three-dimensional box of <volume> $V$, with a uniform positive background replacing the ionic lattice potential. Neglect the detailed periodic potential and explicit electron-electron interactions; the interior one-electron <dispersion relation> is $\epsilon=\hbar^2k^2/(2m_e)$. The boundary confines the particles, and its detailed shape does not affect the bulk state count in a sufficiently large sample.
The <Electrons> are spin-$1/2$ <fermions>: each spatial <quantum state> accommodates two opposite spin states, with occupations given by the <Fermi-Dirac distribution> and the <Pauli exclusion principle>. A fixed number $N$ of conduction <Electrons> and thermal <equilibrium> are assumed. Collisions can be represented by a phenomenological <momentum relaxation time> for transport, but are unnecessary for the equilibrium state counting here. These assumptions distinguish the quantum model from a classical Maxwell-Boltzmann <Electron> gas.
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