Noncommuting Coordinates in the Landau Problem

Abstract

Basic ideas about noncommuting coordinates are summarized, and then coordinate noncommutativity, as it arises in the Landau problem, is investigated. I review a quantum solution to the Landau problem, and evaluate the coordinate commutator in a truncated state space of Landau levels. Restriction to the lowest Landau level reproduces the well known commutator of planar coordinates. Inclusion of a finite number of Landau levels yields a matrix generalization.

9 pages; senior thesis, submitted to the MIT Physics Department on 17 January 2003; email correspondence to [email protected]

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