arXiv:1606.04725 · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Effects on a Landau-type system for a neutral particle with no permanent electric dipole moment subject to the Kratzer potential in a rotating frame

Abinael B. Oliveira, Knut Bakke

Published Jun 1, 2016• 40 citations

Abstract

The behaviour of a neutral particle (atom, molecule) with an induced electric dipole moment in a region with a uniform effective magnetic field under the influence of the Kratzer potential (Kratzer 1920 Z. Phys. 3 , 289–307. ( doi:10.1007/BF01327754 )), and rotating effects is analysed. It is shown that the degeneracy of the Landau-type levels is broken and the angular frequency of the system acquires a new contribution that stems from the rotation effects. Moreover, in the search for bound state solutions, it is shown that the possible values of this angular frequency of the system are determined by the quantum numbers associated with the radial modes and the angular momentum, the angular velocity of the rotating frame and by the parameters associated with the Kratzer potential.

DOI: 10.1098/rspa.2015.0858

Related papers

Some aspects of an induced electric dipole moment in rotating and non-rotating frames

Abinael B. Oliveira, K. Bakke

Quantum effects on a neutral particle (atom or molecule) with an induced electric dipole moment are investigated when it is subject to the Kratzer potential and a scalar potential proportional to the radial distance. In addition, this neutral is placed in a region with electric and magnetic fields. This system is analysed in both non-rotating and rotating reference frames. Then, it is shown that bound state solutions to the Schrödinger equation can be achieved and, in the search for polynomial solutions to the radial wave function, a restriction on the values of the cyclotron frequency is analysed in both reference frames.

arXiv:1706.09251Royal Society Open ScienceJun 1, 201713 citations

Some aspects of the interaction of a magnetic quadrupole moment with an electric field in a rotating frame

I. C. Fonseca, K. Bakke

From the interaction between the magnetic quadrupole moment of a neutral particle (atom or molecule) with a radial electric field, a uniform effective magnetic field perpendicular to the plane of motion of the neutral particle appears. In addition, it is considered that the presence of a scalar potential is proportional to the radial distance and noninertial effects that stem from a rotating reference frame. Then, analytical solutions to the Schrödinger equation are obtained, where it is shown that the Landau-type levels are modified, and the allowed values of the cyclotron frequency are determined by the angular velocity of the rotating frame, the parameter associated with the scalar potential proportional to the radial distance and the quantum numbers of the system.

Journal of Mathematical PhysicsOct 1, 201716 citations

Efeito Aharonov-Casher em potenciais centrais

Priscila Mayana Torres Barboza

In this work, we investigate the system in which a neutral particle with magnetic dipole momentum interacts with an external electric ﬁeld subject to the central potentials, such as scalar potentials proportional to the radial distance and Coulomb like potential. In addition, we analyse the same system when it is conﬁned to a two-dimensional quantum ring and to a quantum dot. In the search for analytical solutions for the Schrödinger-Pauli equation we show that the energy states for this system of a neutral particle subject to the central potentials depend on the quantum geometric phase φAC and the quantum numbers associated with the radial modes, angular momentum, and spin of the system {n, l, s}. Furthermore, we present the quantization of Landau for a neutral particle with a permanent magnetic dipole moment in the presence of external ﬁelds and under the inﬂuence of a Coulomb like potential. We use the idea of Ericsson e Sjöqvist which consists in using the system proposed by Aharonov and Casher to generate an analogue of the quantization of Landau for neutral atom systems. Moreover, we observe that when the analogue of the Landau quantization is subject to a Coulomb like potential its cyclotron frequency is modiﬁed in contrast with the behavior found by of reference. Finally, we discuss the quantum eﬀect characterized by the dependence of quantum numbers with the angular frequency.

Nov 23, 20180 citations

Noncommutative space effects on the Landau system for a neutral particle with induced electric dipole moment under a linear confining potential

Abdelali Saidi, Moulay Brahim Sedra

In this contribution, we study the effects of space noncommutativity on the Landau system for a neutral particle with induced electric dipole moment subject to a linear confining potential. We analytically solve the Schrödinger equation and obtain the complete set of energy levels and the corresponding radial wave functions for the system in terms of the noncommutativity parameter [Formula: see text].

International Journal of Modern Physics AJul 24, 20198 citations

A doubly anharmonic oscillator in an induced electric dipole system

K. Bakke, C. Salvador

The behaviour of the interaction of the induced electric dipole moment of an atom with a uniform magnetic field and a non-uniform electric field are investigated in a rotating reference frame. An interesting aspect of this interaction is that it gives rise to an analogue of a spinless particle subject to the doubly anharmonic oscillator. Then, it is shown that analytical solutions to the Schrödinger equation can be obtained. Another point raised is that the quantum effects on the induced electric dipole moment can be observed if the uniform magnetic field possesses a discrete set of values.

arXiv:1903.02923Proceedings of the Royal Society A Mathematical Physical and Engineering SciencesSep 1, 20186 citations

Efeitos não-inerciais em Anéis Quânticos

Lincoanderson Oliveira Dantas

In this thesis, we investigate by the first time the impact of non-inertial effects associated with the rotation of the reference system on charged and neutral particles confined by a quantum ring, which is described by the potential of Tan-Inkson. The contribution of the rotation is introduced by its coupling with angular momentum of the system. We show that the rotation is introduced via a non-minimum coupling to the kinetic part of the Hamiltonian describing the quantum dynamics of systems studied here. Thus, we show that non-inertial effects of the rotation induce on the quantum properties of the particles similar effects generated by a magnetic field. We also investigated the contribution of a screw dislocation on the physical properties of the particles. The topological defect contributes as a torsion source, presenting a contribution similar to the Aharonov-Bohm flux. Besides charged particles (electrons and holes), we also study the effects of rotation on neutral particles in three different scenarios: a neutral particle with a permanent magnetic dipole moment coupled by the Aharanov-Casher interaction; a neutral particle with a permanent electric dipole moment coupled by the interaction proposed by He-McKellar-Wilkens and a neutral particle with an electric dipole moment induced by the field configuration proposed by Wei-Han-Wei. In all three cases it is shown the similarity between the neutral and charged particles. We analyze the non-relativistic quantum dynamics of these particles by solving the Schrödinger equation. In addition to the energy spectrum and wave functions, we calculate the persistent current and the magnetization for the four systems studied here, and we also analyzed, from the expression for the persistent current for quantum rings, the limit case for quantum dots.

Mar 26, 20150 citations