Relativistic Oscillators in a Noncommutative Space and in a Magnetic Field

Mirza, Behrouz; Narimani, Rasoul; Zare, Somayeh

doi:10.1088/0253-6102/55/3/06

Cited by 56 publications

(41 citation statements)

References 27 publications

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“…It was proposed by Bruce and Minning [45] in analogy with the Dirac oscillator [49] and it has attracted interests in studies of noncommutative space [50,51], in noncommutative phase space [52], in Kaluza-Klein theories [53] and in PT -symmetric Hamiltonian [54]. The relativistic oscillator coupling proposed by Bruce and…”

Section: Klein-gordon Oscillator Under the Effects Of Violation Omentioning

confidence: 99%

A relativistic quantum oscillator subject to a Coulomb-type potential induced by effects of the violation of the Lorentz symmetry

2017

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We consider a background of the violation of the Lorentz symmetry determined by the tensor (K F ) µναβ which governs the Lorentz symmetry violation out of the Standard Model Extension, where this background gives rise to a Coulomb-type potential, and then, we analyse its effects on a relativistic quantum oscillator. Furthermore, we analyse the behaviour of the relativistic quantum oscillator under the influence of a linear scalar potential and this background of the Lorentz symmetry violation. We show in both cases that analytical solutions to the Klein-Gordon equation can be achieved.

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Section: Klein-gordon Oscillator Under the Effects Of Violation Omentioning

confidence: 99%

A relativistic quantum oscillator subject to a Coulomb-type potential induced by effects of the violation of the Lorentz symmetry

2017

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“…Know, we shall review some fundamental principles of the quantum noncommutative Schrödinger equation which resumed in the following steps for modified potential   r V isˆ [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]: …”

Section: Formalism Of Boopp's Shift Metodmentioning

confidence: 99%

“…The Boopp's shift method will be apply in this paper instead of solving the (NC-3D) spaces and phases with star product, the Schrödinger equation will be treated by using directly the two commutators, in addition to usual commutator on quantum mechanics [29][30][31][32][33][34][35][36][37][38][39][40][41]:…”

Section: Introductionmentioning

confidence: 99%

A New Study to the Schrödinger Equation for Modified Potential V(r)=ar2+br-4+cr-6 in Nonrelativistic Three Dimensional Real Spaces and Phases

Maireche

2015

ILCPA

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In present work, by applying Boopp’s shift method and standard perturbation theory we have generated exact nonrelativistic bound states solution for a modified potential (see formula in paper) in both three dimensional noncommutative space and phase (NC: 3D-RSP) at first order of two two infinitesimal parameters antisymmetric (see formula in paper), we have also derived the corresponding noncommutative Hamiltonian.

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“…This coupling is called the Klein-Gordon oscillator [18][19][20][21][22]. In recent years, the Klein-Gordon oscillator has been investigated in noncommutative space [23,24], in noncommutative phase space [25] and in PT -symmetric Hamiltonian [26]. In particular, the isotropic Klein-Gordon oscillator in (2 + 1) dimensions allows us the write the Klein-Gordon equation in the form:…”

Section: Introductionmentioning

confidence: 99%

On a relativistic particle and a relativistic position-dependent mass particle subject to the Klein–Gordon oscillator and the Coulomb potential

2016

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The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed: a dependence of the angular frequency of the KleinGordon oscillator on the quantum numbers of the system. The meaning of this behaviour of the angular frequency is that only some specific values of the angular frequency of the Klein-Gordon oscillator are permitted in order to obtain bound state solutions. As an example, we obtain both the angular frequency and the energy level associated with the ground state of the relativistic system. Further, we analyse the behaviour of an electrically charged particle subject to the Klein-Gordon oscillator, the Coulomb potential and a linear scalar potential.

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Relativistic Oscillators in a Noncommutative Space and in a Magnetic Field

Abstract: In this work, we study the relativistic oscillators in a noncommutative space and in a magnetic field. It is shown that the effect of the magnetic field may compete with that of the noncommutative space and that is able to vanish the effect of the noncommutative space.

Cited by 56 publications

References 27 publications

A relativistic quantum oscillator subject to a Coulomb-type potential induced by effects of the violation of the Lorentz symmetry

A relativistic quantum oscillator subject to a Coulomb-type potential induced by effects of the violation of the Lorentz symmetry

A New Study to the Schrödinger Equation for Modified Potential <i>V(r)=ar<sup>2</sup>+br<sup>-4</sup>+cr<sup>-6</sup></i> in Nonrelativistic Three Dimensional Real Spaces and Phases

On a relativistic particle and a relativistic position-dependent mass particle subject to the Klein–Gordon oscillator and the Coulomb potential

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