The Quantum Spectrum of the 2D Dirac Equation with a Coulomb Potential: Power Series Approach

In this work, we study of the (2+1)-dimensional Dirac oscillator in the presence of a homogeneous magnetic field in an Aharonov-Bohm-Coulomb system. To solve our system, we apply the lef thanded and right-handed projection operators in the Dirac oscillator to obtain a biconfluent Heun equation. Next, we explicitly determine the energy spectrum for the bound states of the system and their exact dependence on the cyclotron frequency ω c and on the parameters Z and Φ AB that characterize the Aharonov-Bohm-Coulomb system. As a result, we observe that by adjusting the frequency of the Dirac oscillator to resonate with the cyclotron half-frequency the energy spectrum reduces to the rest energy of the particle. Also, we determine the exact eigenfunctions, angular frequencies, and energy levels of the Dirac oscillator for the ground state (n = 1) and the first excited state (n = 2). In this case, the energy levels do not depend on the homogeneous magnetic field, and the angular frequencies are real and positive quantities, increase quadratically with the energy and linearly with ω c .

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“…Now, for Φ AB = ω = 0, the Eq. ( 20) is reduced to the (2+1)-dimensional relativistic hydrogen atom [44].…”

Section: Dirac Oscillator In the Presence Of An Homogeneous Mag-netic...mentioning

confidence: 99%

Bound-state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system

Oliveira¹,

Maluf²,

Almeida³

2019

Annals of Physics

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“…For this purpose, researchers have developed various approaches to obtain the exact or numerical solutions of the Schrödinger equation and the Dirac equation for a lot of potentials. Among these methods, the most commonly used techniques are the power series expansion method [1,2], the algebraic method [3], the factorization method [4], the Laplace transformation method [5,6], the path integral method [7][8][9], supersymmetry and shape invariance method [10][11][12][13], WKB as well as supersymmetric WKB (SWKB) methods [14,15]. The developing history of non-relativistic and relativistic quantum mechanics has shown that the emergence of every new method in this field has promoted the development of quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

New features of an asymptotic iteration method for the Dirac equation and their applications

Qiang

Zhang

2006

Phys. Scr.

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We have found that two 'asymptotic' aspects α and β of an asymptotic iteration method for the Dirac equation satisfy nonlinear Riccati equations simultaneously and are reciprocal to each other. By these two properties, we have an insight into this method and reveal why this method can give solutions to the Dirac equation. Furthermore, using the new iteration termination condition expressed by equation ( 15), instead of solving the differential equations directly, we have found exact eigenvalues as well as exact wavefunctions of the Dirac equation with two dimensional Coulomb potential.

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Perturbed Coulomb Potentials in the Klein–Gordon Equation: Quasi-Exact Solution

Baradaran

Panahi

2018

Few-Body Syst

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The Quantum Spectrum of the 2D Dirac Equation with a Coulomb Potential: Power Series Approach

Abstract: The two-dimensional Dirac equation with a Coulomb potential has been studied by the power series expansion method. The eigenfunctions expressed by the confluent hypergeometric functions are analytically obtained. The eigenvalues and their fine structures of this system are also studied.

Cited by 9 publications

References 29 publications

Bound-state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system

Bound-state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system

New features of an asymptotic iteration method for the Dirac equation and their applications

Perturbed Coulomb Potentials in the Klein–Gordon Equation: Quasi-Exact Solution

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