Bloch theorem

Bloch theorem [′bläk ‚thir·əm]

(quantum mechanics)

The theorem that the lowest state of a quantum-mechanical system without a magnetic field can carry no current.

(solid-state physics)

The theorem that, in a periodic structure, every electronic wave function can be represented by a Bloch function.

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Bloch theorem

A theorem that specifies the form of the wave functions that characterize electron energy levels in a periodic crystal. Electrons that move in a constant potential, that is, a potential independent of the position r , have wave functions that are plane waves, having the form exp(i k · r ). Here, k is the wave vector, which can assume any value, and describes an electron having momentum ℏ k . (The quantity ℏ is Planck's constant divided by 2&pgr;.) Electrons in a crystal experience a potential that has the periodicity of the crystal lattice. See Band theory of solids