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

This article is cited in 14 scientific papers (total in 14 papers)

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
b Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47071 Valladolid, Spain

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.


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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

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
\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

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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  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Tezuka H., “Analytical Solutions of the Dirac Equation with a Scalar Linear Potential”, AIP Adv., 3:8 (2013), 082135  crossref  adsnasa  isi  scopus
    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  crossref  mathscinet  isi  elib  scopus
    4. Mielnik B., “Quantum Operations: Technical Or Fundamental Challenge?”, J. Phys. A-Math. Theor., 46:38 (2013), 385301  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    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  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Yesiltas O., “Exact Solutions of the Dirac Hamiltonian on the Sphere Under Hyperbolic Magnetic Fields”, Adv. High. Energy Phys., 2014, 186425  crossref  mathscinet  isi  elib  scopus
    7. Contreras-Astorga A., Schulze-Halberg A., “the Confluent Supersymmetry Algorithm For Dirac Equations With Pseudoscalar Potentials”, J. Math. Phys., 55:10 (2014), 103506  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    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  crossref  mathscinet  isi  scopus
    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  crossref  zmath  adsnasa  isi  elib  scopus
    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  crossref  zmath  isi  elib  scopus
    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  crossref  isi  scopus
    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  isi
    13. A. Schulze-Halberg, O. Yesiltas, “The generalized confluent supersymmetry algorithm: representations and integral formulas”, J. Math. Phys., 59:4 (2018), 043508  crossref  mathscinet  zmath  isi  scopus
    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  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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