On the solution of a “2D Coulomb + Aharonov-Bohm” problem: oscillator strengths in the discrete spectrum and scattering

Nguyen, Hang Thi; Meleshenko, Peter A.; Dolgikh, A. V.; Klinskikh, A. F.

doi:10.1140/epjd/e2011-10726-y

Cited by 11 publications

(13 citation statements)

References 27 publications

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“…[67,70,80]. In the absence of the spin degree of freedom, we recover the result for the case of regular solution at the origin [81].…”

Section: Discussion Of the Resultssupporting

confidence: 77%

Effects of rotation and Coulomb type potential on the spin-1/2 Aharonov-Bohm problem

Cunha¹,

Andrade²,

Silva³

2021

Preprint

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In this work, we investigate how both rotation and a Coulomb potential affect the quantum mechanical description of a spin-1/2 particle in the presence of the Aharonov-Bohm effect. We employ the method of the self-adjoint extensions in the framework of the Pauli-Schrödinger equation. We discuss the role of the spin degree of freedom on this problem, find the energy spectrum, and investigate the results in detail.

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“…[67,70,80]. In the absence of the spin degree of freedom, we recover the result for the case of regular solution at the origin [81].…”

Section: Discussion Of the Resultssupporting

confidence: 77%

Effects of rotation and Coulomb type potential on the spin-1/2 Aharonov-Bohm problem

Cunha¹,

Andrade²,

Silva³

2021

Preprint

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“…Let us now consider the configurations of the vector potential of the AB effect and of the 2D Coulomb potential. Explicitly, these configurations are given in the form [9][10][11][12]21]…”

Section: The Dirac Equation With Position-dependent Mass In An Aharon...mentioning

confidence: 99%

“…The in literature, there a significant number of works that investigate the dynamics of particles with constant mass interacting with the vector potential of the Aharonov-Bohm (AB) effect [1][2][3][4] and the 2D Coulomb potential [5][6][7][8]. A system described by the combination of these two potentials is so-called Aharonov-Bohm-Coulomb (ABC) system [9][10][11][12]. In particular, the ABC system for spin-1/2 relativistic particles is studied in connection with the Feynman path integrals [14,15], scattering [16], magnetic monopole [17,18], spontaneous creation of fermions pairs [19], Coulomb impurity [20], etc.…”

Section: Introductionmentioning

confidence: 99%

The relativistic Aharonov–Bohm–Coulomb system with position-dependent mass

Oliveira¹,

Filho²,

Maluf³

et al. 2020

J. Phys. A: Math. Theor.

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In this work, we study the Aharonov-Bohm-Coulomb (ABC) system for a relativistic Dirac particle with position-dependent mass (PDM). To solve our system, we use the lef t-handed and right-handed projection operators. Next, we explicitly obtain the eigenfunctions and the energy spectrum of the particle. We verify that these eigenfunctions are written in terms of the generalized Laguerre polynomials and the energy spectrum depends on the parameters Z, Φ AB and κ. We notice that the parameter κ has the function of increasing the values of the energy levels of the system. In addition, the usual ABC system is recovered when one considers the limit of constant mass (κ → 0). Moreover, also we note that even in the absence of ABC system (Z = Φ AB = 0), the particle with PDM still has a discrete energy spectrum.

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“…An interest in including a Coulomb-type potential comes from the studies of quark models [32,33], the Kratzer potential [34], the Mie-type potential [35], position-dependent mass systems [36][37][38] and topological defects in solids [39][40][41][42][43]. Recently, the two-dimensional Coulomb potential has been investigated under the presence of the AharonovBohm effect [44][45][46]. According to Ref.…”

Section: Quantum Dynamics Of a Spin-half Neutral Particlementioning

confidence: 99%

An angular frequency dependence on the Aharonov–Casher geometric phase

Barboza

Bakke

2015

Annals of Physics

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A quantum effect characterized by a dependence of the angular frequency associated with the confinement of a neutral particle to a quantum ring on the quantum numbers of the system and the Aharonov-Casher geometric phase is discussed. Then, it is shown that persistent spin currents can arise in a two-dimensional quantum ring in the presence of a Coulomb-type potential. A particular contribution to the persistent spin currents arises from the dependence of the angular frequency on the geometric quantum phase.

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On the solution of a “2D Coulomb + Aharonov-Bohm” problem: oscillator strengths in the discrete spectrum and scattering

Cited by 11 publications

References 27 publications

Effects of rotation and Coulomb type potential on the spin-1/2 Aharonov-Bohm problem

Effects of rotation and Coulomb type potential on the spin-1/2 Aharonov-Bohm problem

The relativistic Aharonov–Bohm–Coulomb system with position-dependent mass

An angular frequency dependence on the Aharonov–Casher geometric phase

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