Bloch theorem

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

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.

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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
If a time-periodic field is applied to electrons in a periodic lattice the Bloch theorem can be applied twice, both in space and in time.
Using a version of Koebe theorem for analytic functions (we can also use Bloch theorem), we outline a proof.
(1) the Bloch theorem can be applied for the x-direction.