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Energy spectrum for bloch electrons in a magnetic field
Author(s) -
Wannier Gregory H.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560160842
Subject(s) - physics , electron , field (mathematics) , magnetic field , landau quantization , energy spectrum , spectrum (functional analysis) , theoretical physics , quantum mechanics , energy (signal processing) , quantum electrodynamics , classical mechanics , statistical physics , mathematics , pure mathematics
Recent progress on the quantum mechanics of a charged particle moving in a periodic potential under the influence of a magnetic field is reviewed. The study of this problem has been retarded by the great success of the Peierls‐Onsager approximation and its quasiclassical simplification. It is found that the Landau levels are one aspect of a much richer structure. In two fully worked out examples, it is shown that theoretical need to assume that the field is rational is compatible with an energy spectrum which varies continuously with the field, and can be represented pictorially.