THE LANDAU PROBLEM AND NONCOMMUTATIVE QUANTUM MECHANICS
Задача Ландау и некоммутативная квантовая механика
2001-10-20
SCID: 54.1/kfg8k43s
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Landau problemlowest Landau levelnoncommutative effectsnoncommutative quantum mechanicsphysical bounds
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Abstract (AI)
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.
Key Findings
1
Different physical systems can yield different values of the noncommutative parameter, so its bounds should be determined through a system-independent physical scenario.
2
Noncommutative quantum mechanics with potential V=Ωℵ is equivalent to the Landau problem in the lowest Landau level for a specific value of the noncommutative parameter.
3
System-dependent parameter values may explain the differing bounds reported for noncommutative effects in the literature.
Research Object
the equivalence between noncommutative quantum mechanics and the Landau problem in the lowest Landau level
Research Subject
the conditions and bounds on the noncommutative parameter under which the two theories are equivalent, including the role of the potential choice
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2001-10-20
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