Physics – General Physics
Scientific paper
2011-11-25
Physics
General Physics
7 pages, 1 figure
Scientific paper
The problem of a single electron in a magnetic field is revisited from first principles. It is shown that the quantization used by Landau was inconsistent, and that his formal solution is but a single Fourier component of the physical one, derived here. Canonical quantization removes the infinite degeneracy in a second quantum number, characteristic of many current treatments of the problem in the literature. The present approach properly accounts for the loss of translation invariance, which occurs because the electron has to move on a circle, whose center is static, but not known in advance. The translations in the plane appear as a distinct gauge group, in addition to the electromagnetic one. Previous research which made explicit use of Landau's wave functions is not automatically invalidated, but may need to be reviewed, in some cases, in the light of this result. In particular, Landau's own estimate of the one-particle density of states of electrons in a magnetic field remains standing.
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