Variations on the Planar Landau Problem: Canonical Transformations, A Purely Linear Potential and the Half-Plane

Physics – High Energy Physics – High Energy Physics - Theory

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Scientific paper

10.1088/1751-8113/42/48/485209

The ordinary Landau problem of a charged particle in a plane subjected to a perpendicular homogeneous and static magnetic field is reconsidered from different points of view. The role of phase space canonical transformations and their relation to a choice of gauge in the solution of the problem is addressed. The Landau problem is then extended to different contexts, in particular the singular situation of a purely linear potential term being added as an interaction, for which a complete purely algebraic solution is presented. This solution is then exploited to solve this same singular Landau problem in the half-plane, with as motivation the potential relevance of such a geometry for quantum Hall measurements in the presence of an electric field or a gravitational quantum well.

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