Band Spectrum in a Periodic Potential

Plot of the symmetric solution of .


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is the energy.
The spectrum of the Schrödinger operator with a periodic potential has allowed energy bands. When the energy is within a band, the eigenfunctions are the product of a phase factor of magnitude 1 and periodic parts. As a result, the eigenfunctions are -normalizable. When the energy is outside the bands, the eigenfunctions grow unbounded as . You can see both situations by varying the energy.
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