Exact Solutions of the Dirac Hamiltonian on the Sphere under Hyperbolic Magnetic Fields
Two-dimensional massless Dirac Hamiltonian under the influence of hyperbolic magnetic fields is mentioned in curved space. Using a spherical surface parameterization, the Dirac operator on the sphere is presented and the system is given as two supersymmetric partner Hamiltonians which coincides with...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2014/186425 |
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| author | Özlem Yeşiltaş |
| author_facet | Özlem Yeşiltaş |
| author_sort | Özlem Yeşiltaş |
| collection | DOAJ |
| description | Two-dimensional massless Dirac Hamiltonian under the influence of hyperbolic magnetic fields is mentioned in curved space. Using a spherical surface parameterization, the Dirac operator on the sphere is presented and the system is given as two supersymmetric partner Hamiltonians which coincides with the position dependent mass Hamiltonians. We introduce two ansatzes for the component of the vector potential to acquire effective solvable models, which are Rosen-Morse II potential and the model given Midya and Roy, whose bound states are Jacobi X1 type polynomials, and we adapt our work to these special models under some parameter restrictions. The energy spectrum and the eigenvectors are found for Rosen-Morse II potential. On the other hand, complete solutions are given for the second system. The vector and the effective potentials with their eigenvalues are sketched for each system. |
| format | Article |
| id | doaj-art-b4810b5f4d3b436c8ffaad30fefc14d4 |
| institution | Kabale University |
| issn | 1687-7357 1687-7365 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-b4810b5f4d3b436c8ffaad30fefc14d42025-02-03T00:59:31ZengWileyAdvances in High Energy Physics1687-73571687-73652014-01-01201410.1155/2014/186425186425Exact Solutions of the Dirac Hamiltonian on the Sphere under Hyperbolic Magnetic FieldsÖzlem Yeşiltaş0Department of Physics, Faculty of Science, Gazi University, 06500 Ankara, TurkeyTwo-dimensional massless Dirac Hamiltonian under the influence of hyperbolic magnetic fields is mentioned in curved space. Using a spherical surface parameterization, the Dirac operator on the sphere is presented and the system is given as two supersymmetric partner Hamiltonians which coincides with the position dependent mass Hamiltonians. We introduce two ansatzes for the component of the vector potential to acquire effective solvable models, which are Rosen-Morse II potential and the model given Midya and Roy, whose bound states are Jacobi X1 type polynomials, and we adapt our work to these special models under some parameter restrictions. The energy spectrum and the eigenvectors are found for Rosen-Morse II potential. On the other hand, complete solutions are given for the second system. The vector and the effective potentials with their eigenvalues are sketched for each system.http://dx.doi.org/10.1155/2014/186425 |
| spellingShingle | Özlem Yeşiltaş Exact Solutions of the Dirac Hamiltonian on the Sphere under Hyperbolic Magnetic Fields Advances in High Energy Physics |
| title | Exact Solutions of the Dirac Hamiltonian on the Sphere under Hyperbolic Magnetic Fields |
| title_full | Exact Solutions of the Dirac Hamiltonian on the Sphere under Hyperbolic Magnetic Fields |
| title_fullStr | Exact Solutions of the Dirac Hamiltonian on the Sphere under Hyperbolic Magnetic Fields |
| title_full_unstemmed | Exact Solutions of the Dirac Hamiltonian on the Sphere under Hyperbolic Magnetic Fields |
| title_short | Exact Solutions of the Dirac Hamiltonian on the Sphere under Hyperbolic Magnetic Fields |
| title_sort | exact solutions of the dirac hamiltonian on the sphere under hyperbolic magnetic fields |
| url | http://dx.doi.org/10.1155/2014/186425 |
| work_keys_str_mv | AT ozlemyesiltas exactsolutionsofthedirachamiltonianonthesphereunderhyperbolicmagneticfields |