Abstract
The energy spectrum of an electron in the simultaneous presence of an external magnetic field \( {\text{H}} \) and a periodic crystal potential \( V\left( {\vec r} \right)\) constitutes a difficult and by now classical problem. It is difficult because the effects of the potential \( V\left( {\vec r} \right)\) and the field H are quite different in nature. The former causes the formation of energy bands while the latter quantizes the electronic motion and tends to form narrow levels. The problem is further complicated by the fact that the two natural “periods,” introduced by the field H and the potential \( V\left( {\vec r} \right)\), respectively, are, for most values of the field, incommensurable.
Work supported in part by The National Science Foundation through Grant No. DMR78-03408.
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Falicov, L.M. (1980). Level Quantization and Broadening for Band Electrons in a Magnetic Field: Magneto-Optics Throughout the Band. In: Devreese, J.T. (eds) Theoretical Aspects and New Developments in Magneto-Optics. Nato Advanced Study Institutes Series, vol 60. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0454-6_1
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