THE LANDAU PROBLEM AND NONCOMMUTATIVE QUANTUM MECHANICS

Abstract

We explore the conditions under which noncommutative quantum mechanics and the Landau problem are equivalent theories. If the potential in noncommutative quantum mechanics is chosen as V=Ωℵ with ℵ defined in the text, then for the value [Formula: see text] (which measures the noncommutative effects of the space), the Landau problem and noncommutative quantum mechanics are equivalent theories in the lowest Landau level. For other systems one can find different values for [Formula: see text] and, therefore, the possible bounds for [Formula: see text] should be searched in a physical independent scenario. This last fact could explain the different bounds for [Formula: see text] found in the literature.