The Landau problem in non-commutative quantum mechanics （NCQM） is studied. First by solving the SchrSdinger equations on noncommutative （NC） space we obtain the Landau energy levels and the energy correction that is caused by space-space noncommutativity. Then we discuss the noncommutative phase space case, namely, space-space and momentum-momentum non-commutative case, and we get the explicit expression of the Hamiltonian as well as the corresponding eigenfunctions and eigenvalues.
A new particle Σ^ ＊ with J ^P = 1/2^-was predicted by unquenched quark models with its mass around the well established Σ ＊ （1385） with J P = 3/2 ＋ .Here we re-examine some old data of the K^-p → Λπ^-π^ ＋ reaction.Firstly we re-fit the data for kaon beam momenta in the range of 1.0 - 1.8 GeV.Secondly we study the reaction at the energies around Λ＊（1520） peak.Both studies show evidence for the existence of Σ＊with J^ P = 1/2^-around 1380 MeV.Higher statistic data on relevant reactions are needed to clarify the situation.
We study the Klein-Gordon oscillators in non-commutative （NC） phase space. We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field. By solving the Klein-Gordon equation in NC phase space, we obtain the energy levels of the Klein-Gordon oscillators, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.
By using star product method, the He-McKellar-Wilkens （HMW） effect for spin-one neutral particle on noncommutative （NC） space is studied. After solving the Kemmer-like equations on NC space, we obtain the topological HMW phase on NC space where the additional terms related to the space-space non-commutativity are given explicitly.
