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On uncertainty relations in noncommutative quantum mechanics

“…for some γ ∈ R. Multiplying both sides of eq. ( 10) by  − A ψ I and using again (10) as well as the saturated version of ( 8) we obtain, provided γ = 0,…”

Landau problem in noncommutative quantum mechanics

“…It appears that the most natural places to search the noncommutativity effects are simple quantum mechanics (QM) system. So far many interesting topics in NCQM such as hydrogen atom spectrum in an external magnetic field [10,11], Aharonov-Bohm(AB) effect [12] in the presence of the magnetic field, the Aharonov-Casher effects [13], and Landau problem [14], as well as the Van de Waals interactions and photoelectric effect in noncommutative quantum mechanics [15] have been studied extensively. The purpose of this paper is to study the Landau problems on NC space and NC phase space, respectively, where both space-space and momentum-momentum noncommutativity could give additional contribution.…”

The Aharonov–Bohm effect in noncommutative quantum mechanics

“…It appears that the most natural places to search the noncommutativity effects are simple quantum mechanics (QM) system. So far many interesting topics in NCQM such as hydrogen atom spectrum in an external magnetic field [12,15] and Aharonov-Bohm(AB) effect [14] in the presence of the magnetic field, as well as the Aharonov-Casher effects [16] have been studied extensively. The purpose of this paper is to do further study on the Aharonov-Bohm effect on NC space and NC phase space, respectively, where the space-space noncommutativity and both space-space and momentum-momentum noncommutativity could produce additional phase difference.…”