Band Spectrum in a Periodic Potential

— 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.