Abstract
A quantum-mechanical representation is defined by means of finite translations in direct and reciprocal space. The eigenfunctions of the finite translations are found and their connection with Bloch functions and Wannier functions is established. The new representation is used for describing the motion of a Bloch electron in a magnetic and in an electric field. For the first problem, well-known results are reproduced in an extremely simple and natural way. It is also shown that the representation introduced in this paper gives a straightforward way to compare classical and quantum dynamics for a Bloch electron in external magnetic and electric fields.
Keywords
PhysicsElectronEigenfunctionMagnetic fieldClassical mechanicsQuantum mechanicsRepresentation (politics)Electric fieldEigenvalues and eigenvectors
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Publication Info
- Year
- 1968
- Type
- article
- Volume
- 168
- Issue
- 3
- Pages
- 686-695
- Citations
- 183
- Access
- Closed
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Cite This
J. Żak
(1968).
Dynamics of Electrons in Solids in External Fields.
Physical Review
, 168
(3)
, 686-695.
https://doi.org/10.1103/physrev.168.686
Identifiers
- DOI
- 10.1103/physrev.168.686