Jan Govaerts et al 2009 J. Phys. A: Math. Theor. 42 485209 doi:10.1088/1751-8113/42/48/485209
Jan Govaerts1,2,4, M Norbert Hounkonnou2 and Habatwa V Mweene3
Show affiliationsThe 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.
04.60.Ds Canonical quantization
83C45 Quantization of the gravitational field
Issue 48 (4 December 2009)
Received 14 September 2009
Published 17 November 2009
Jan Govaerts et al 2009 J. Phys. A: Math. Theor. 42 485209
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