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 SIGMA, 2012, Volume 8, 082, 10 pages (Mi sigma759)

Solutions of the Dirac equation in a magnetic field and intertwining operators

Alonso Contreras-Astorgaa, David J. Fernández C.a, Javier Negrob

a Departamento de Física, Cinvestav, AP 14-740, 07000 México DF, Mexico

Abstract: The intertwining technique has been widely used to study the Schrödinger equation and to generate new Hamiltonians with known spectra. This technique can be adapted to find the bound states of certain Dirac Hamiltonians. In this paper the system to be solved is a relativistic particle placed in a magnetic field with cylindrical symmetry whose intensity decreases as the distance to the symmetry axis grows and its field lines are parallel to the $x-y$ plane. It will be shown that the Hamiltonian under study turns out to be shape invariant.

Keywords: intertwining technique; supersymmetric quantum mechanics; Dirac equation.

DOI: https://doi.org/10.3842/SIGMA.2012.082

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ArXiv: 1210.7416
MSC: 81Q05; 81Q60; 81Q80
Received: July 31, 2012; in final form October 17, 2012; Published online October 28, 2012
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Citation: Alonso Contreras-Astorga, David J. Fernández C., Javier Negro, “Solutions of the Dirac equation in a magnetic field and intertwining operators”, SIGMA, 8 (2012), 082, 10 pp.

Citation in format AMSBIB
\Bibitem{ConFerNeg12} \by Alonso Contreras-Astorga, David J. Fern\'andez C., Javier Negro \paper Solutions of the Dirac equation in a magnetic field and intertwining operators \jour SIGMA \yr 2012 \vol 8 \papernumber 082 \totalpages 10 \mathnet{http://mi.mathnet.ru/sigma759} \crossref{https://doi.org/10.3842/SIGMA.2012.082} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3007277} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000312377600001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84869066744} 

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This publication is cited in the following articles:
1. Jakubsky V., “Applications of the Potential Algebras of the Two-Dimensional Dirac-Like Operators”, Ann. Phys., 331 (2013), 216–235
2. Tezuka H., “Analytical Solutions of the Dirac Equation with a Scalar Linear Potential”, AIP Adv., 3:8 (2013), 082135
3. Schulze-Halberg A., “Darboux Operators for Linear First-Order Multi-Component Equations in Arbitrary Dimensions”, Cent. Eur. J. Phys., 11:4 (2013), 457–469
4. Mielnik B., “Quantum Operations: Technical Or Fundamental Challenge?”, J. Phys. A-Math. Theor., 46:38 (2013), 385301
5. Aghaei S., Chenaghlou A., “Dirac Equation and Some Quasi-Exact Solvable Potentials in the Turbiner's Classification”, Commun. Theor. Phys., 60:3 (2013), 296–302
6. Yesiltas O., “Exact Solutions of the Dirac Hamiltonian on the Sphere Under Hyperbolic Magnetic Fields”, Adv. High. Energy Phys., 2014, 186425
7. Contreras-Astorga A., Schulze-Halberg A., “the Confluent Supersymmetry Algorithm For Dirac Equations With Pseudoscalar Potentials”, J. Math. Phys., 55:10 (2014), 103506
8. Contreras-Astorga A., “One Dimensional Dirac-Moshinsky Oscillator-Like System and Isospectral Partners”, International conference on quantum control, exact or perturbative, linear or nonlinear to celebrate 50 years of the scientific career of professor bogdan mielnik (mielnik50), Journal of Physics Conference Series, 624, eds. Breton N., Fernandez D., Kielanowski P., IOP Publishing Ltd, 2015, 012013
9. Contreras-Astorga A., Negro J., Tristao S., “Confinement of An Electron in a Non-Homogeneous Magnetic Field: Integrable Vs Superintegrable Quantum Systems”, Phys. Lett. A, 380:1-2 (2016), 48–55
10. Shojaei M.R., Mousavi M., “the Effect of Tensor Interaction in Splitting the Energy Levels of Relativistic Systems”, Adv. High. Energy Phys., 2016, 8314784
11. M. Mousavi, M. R. Shojaei, “Bound-state energy of double magic number plus one nucleon nuclei with relativistic mean-field approach”, Pramana-J. Phys., 88:2 (2017), 21
12. M. Mousavi, M. R. Shojaei, “Relativistic solution of eckart plus hulthen potentials in the presence of spin and pseudospin symmetry”, Indian J. Pure Appl. Phys., 56:3 (2018), 218–225
13. A. Schulze-Halberg, O. Yesiltas, “The generalized confluent supersymmetry algorithm: representations and integral formulas”, J. Math. Phys., 59:4 (2018), 043508
14. Ishkhanyan A., Jakubsky V., “Two-Dimensional Dirac Fermion in Presence of An Asymmetric Vector Potential”, J. Phys. A-Math. Theor., 51:49 (2018), 495205
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