X-Nico

Band mapping

The electronic states in the solid are described by energy bands, which have associated energy band dispersions E(k) — energy eigenvalues for delocalized electrons in a crystalline medium according to Bloch's theorem.

Bloch wave

Other much studied periodic one-dimensional equations are the Kronig–Penney model and Mathieu's equation.

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The same underlying mathematics, however, was also discovered independently several times: by George William Hill (1877), Gaston Floquet (1883), and Alexander Lyapunov (1892).

Bloch's theorem

For the theorem named after Felix Bloch on wave functions of a particle in a periodic potential, see Bloch wave.

see also