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Bloch Theorem

Atomic section generated from Complete Solid State Physics.

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Bloch Theorem

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Bloch Theorem

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

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

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

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