Bloch electrons in a magnetic field: Reduction to one dimension
- 1 December 1980
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 21 (12) , 2844-2846
- https://doi.org/10.1063/1.524384
Abstract
A reduction to one dimension of the above problem, found by Schellnhuber and Obermair for a special model lattice, is shown to be valid for all lattices without restriction. As was the case in their problem, the field must be rational. If the rational number is the reciprocal of an integer a single equation results. This condition is well adapted to the study of fields of practically attainable magnitude. If the rational number is of the form q/p a system of q coupled equations is obtained.Keywords
This publication has 4 references indexed in Scilit:
- First-Principles Calculation of Diamagnetic Band StructurePhysical Review Letters, 1980
- Quantum Numbers for Bloch Electrons in a Magnetic FieldPhysica Status Solidi (b), 1980
- Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fieldsPhysical Review B, 1976
- Bloch Electrons in Irrational Magnetic FieldsPhysica Status Solidi (b), 1974