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Advances in High Energy Physics
Volume 2014, Article ID 186425, 8 pages
http://dx.doi.org/10.1155/2014/186425
Research Article

Exact Solutions of the Dirac Hamiltonian on the Sphere under Hyperbolic Magnetic Fields

Department of Physics, Faculty of Science, Gazi University, 06500 Ankara, Turkey

Received 5 April 2014; Accepted 11 June 2014; Published 1 July 2014

Academic Editor: Filipe R. Joaquim

Copyright © 2014 Özlem Yeşiltaş. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Abstract

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 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.