Quantum bound states of a Landau-type system for a moving electric quadrupole moment under the Kratzer potential in both
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Quantum bound states of a Landau-type system for a moving electric quadrupole moment under the Kratzer potential in both commutative and noncommutative spaces Abdelali Saidi1,a
, Moulay Brahim Sedra1,2,b
1 Simo-Lab, Department of Physics, Faculty of Sciences, Ibn Tofail University, Kenitra, Morocco 2 Faculty of Sciences and Techniques, Moulay Ismail University, BP 509, Boutalamine, 52000 Errachidia,
Morocco Received: 15 July 2020 / Accepted: 17 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Bound states solutions and radial wave functions of a Landau system for a moving neutral particle that possesses an electric quadrupole moment under the Kratzer potential are obtained in commutative and noncommutative spaces. In both spaces, it is shown that the energy levels of bound states and the angular frequency are modified and become determined by the quantum numbers of the system, the parameters associated with the Kratzer potential, and particularly by the noncommutativity parameter θ for the case of noncommutative spaces. The noncommutative corrections to the energy levels of bound states due to space noncommutativity effects are also obtained using the first-order perturbation theory.
1 Introduction The study of quantum dynamics of particle systems that possess quadrupole moments has attracted a great deal of attention in recent years. The interaction between quadrupole moments of neutral particles and external electromagnetic fields has been applied to many different contexts: nuclear physics [1,2], atomic and molecular structures [3–10], geometric quantum phases [11], and Landau quantization [12–14]. In particular, the study of quantum effects arising from the interaction between an electric quadrupole moment, considered in this study, and external fields has also been made in the current literature. The authors of Ref. [11] have shown that the interaction between the electric quadrupole moment of a neutral particle and a magnetic field gives rise to the appearance of a geometric quantum phase. The arising of an analogue of the Coulomb potential associated with the interaction between a moving electric quadrupole moment and a magnetic field has been achieved in Ref. [15]. Recently, an analogue of the scalar Aharonov–Bohm effect has been obtained in Ref. [16], which arises from the interaction between an electric field and the electric quadrupole moment of a neutral particle. On the other hand, a particular interest has been devoted to study of Landau quantization for neutral particles. Lemos de Melo et al. [12] have proposed the
a e-mail: [email protected] (corresponding author) b e-mail: [email protected]
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Landau quantization for neutral particles possessing an electric quadrupole moment. They have discussed some conditions on field configurations in the quadrupole system in order to achieve the Landau quantization. An important study on the Landau quantizati
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