Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators
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 ma...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148666 |
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| Zitieren: | Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators / A. Contreras-Astorga, D. J. Fernández C., J. Negro // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862737363515473920 |
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| author | Contreras-Astorga, A. J. Fernández C., D. Negro, J. |
| author_facet | Contreras-Astorga, A. J. Fernández C., D. Negro, J. |
| citation_txt | Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators / A. Contreras-Astorga, D. J. Fernández C., J. Negro // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T19:58:26Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148666 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:58:26Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Contreras-Astorga, A. J. Fernández C., D. Negro, J. 2019-02-18T17:44:02Z 2019-02-18T17:44:02Z 2012 Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators / A. Contreras-Astorga, D. J. Fernández C., J. Negro // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81Q05; 81Q60; 81Q80 DOI: http://dx.doi.org/10.3842/SIGMA.2012.082 https://nasplib.isofts.kiev.ua/handle/123456789/148666 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. This paper is a contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”. The full collection is available at http://www.emis.de/journals/SIGMA/SESSF2012.html.
 We acknowledge financial support from Ministerio de Ciencia e Innovaci´on (MICINN) of Spain, projects MTM2009-10751, and FIS2009-09002. ACA acknowledges to Conacyt a PhD grant and the kind hospitality at University of Valladolid. DJFC acknowledges the financial support of Conacyt, project 152574. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators Article published earlier |
| spellingShingle | Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators Contreras-Astorga, A. J. Fernández C., D. Negro, J. |
| title | Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators |
| title_full | Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators |
| title_fullStr | Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators |
| title_full_unstemmed | Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators |
| title_short | Solutions of the Dirac Equation in a Magnetic Field and Intertwining Operators |
| title_sort | solutions of the dirac equation in a magnetic field and intertwining operators |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148666 |
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