Variations on the planar Landau problem : canonical transformations, a purely linear potential and the half-plane
(2009) Journal of Physics A: Mathematical and Theoretical —
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- Authors
Govaerts, Jan 
- Abstract
- (en) 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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Citations
Govaerts, J., Hounkonnou, M. N., & Mweene, H. V. (2009). Variations on the planar Landau problem : canonical transformations, a purely linear potential and the half-plane. Journal of Physics A: Mathematical and Theoretical. https://hdl.handle.net/2078.5/257240