engleski

Angular momentum in two dimensions

It is shown by direct computation that angular momentum cannot be reduced to two dimensions by assuming lack of dependence on the z coordinate. Formally, this is because independence of z breaks rotational invariance. As a physical example, it is shown that a gauge- and rotation-invariant description of planar electrons in a perpendicular magnetic field must have a three-dimensional form, even though all the terms refer to planar coordinates alone. The physical concepts underlying common formal manipulations with the quantum angular momentum operator are treated at a level directly useful to students encountering them thoroughly for the first time. The paper may also serve as a contextual introduction to advanced quantization issues, usually studied at graduate level.

angular momentum; magnetic field

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