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\title{Complete Solid State Physics: Bloch Theorem}
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\section{Bloch Theorem}

For a periodic potential $V(\mathbf r+\mathbf R)=V(\mathbf r)$, one-particle
eigenstates can be written

$$
\psi_{n\mathbf k}(\mathbf r)=e^{i\mathbf k\cdot\mathbf r}u_{n\mathbf k}(\mathbf r),
$$

where $u_{n\mathbf k}$ has the periodicity of the lattice.

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