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

Journal Article · Tue Jan 15 04:00:00 EST 2019 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2018.11.005· OSTI ID:22852370

Oliveira, R. R.S.,; Almeida, C. A.S., ^[1]

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1. Universidade Federal do Ceará (UFC), Departamento de Física, Campus do Pici, Fortaleza - CE, C.P. 6030, 60455-760 (Brazil)

In this work, we study 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 left-handed 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{sub c} and on the parameters Z and Φ{sub 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{sub c}.

• OSTI ID: 22852370
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 400; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AHARONOV-BOHM EFFECT
BOUND STATE
CYCLOTRON FREQUENCY
EIGENFUNCTIONS
ENERGY SPECTRA
EQUATIONS
EXCITED STATES
GROUND STATES
MAGNETIC FIELDS
MATHEMATICAL SOLUTIONS
OSCILLATORS