%0 Journal Article %1 WOS:000460086700001 %A Oliveira, R R S %A Maluf, R V %A Almeida, C A S %C 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA %D 2019 %I ACADEMIC PRESS INC ELSEVIER SCIENCE %J ANNALS OF PHYSICS %K Aharonov-Bohm-Coulomb Biconfluent Heun Relativistic bound equation; oscillator; states} system; {Dirac %P 1-8 %R 10.1016/j.aop.2018.11.005 %T Bound-state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system %V 400 %X 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 omega(c) and on the parameters Z and Phi(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 omega(c). (C) 2018 Elsevier Inc. All rights reserved.

@article{WOS:000460086700001, abstract = {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 omega(c) and on the parameters Z and Phi(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 omega(c). (C) 2018 Elsevier Inc. All rights reserved.}, added-at = {2022-05-23T20:00:14.000+0200}, address = {525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA}, author = {Oliveira, R R S and Maluf, R V and Almeida, C A S}, biburl = {https://www.bibsonomy.org/bibtex/27d629153c4f3b603eca168c607331ec6/ppgfis_ufc_br}, doi = {10.1016/j.aop.2018.11.005}, interhash = {7456a1863b6474939650de65076e830c}, intrahash = {7d629153c4f3b603eca168c607331ec6}, issn = {0003-4916}, journal = {ANNALS OF PHYSICS}, keywords = {Aharonov-Bohm-Coulomb Biconfluent Heun Relativistic bound equation; oscillator; states} system; {Dirac}, pages = {1-8}, publisher = {ACADEMIC PRESS INC ELSEVIER SCIENCE}, pubstate = {published}, timestamp = {2022-05-23T20:00:14.000+0200}, title = {Bound-state solutions of the Dirac oscillator in an Aharonov-Bohm-Coulomb system}, tppubtype = {article}, volume = 400, year = 2019 }