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Advances in Mathematical Physics
Volume 2012 (2012), Article ID 762908, 13 pages
Research Article

Relativistic Double Barrier Problem with Three Transmission Resonance Regions

1Saudi Center for Theoretical Physics, Dhahran, Saudi Arabia
2Physics Department, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia
3Physics Department, College of Science, King Faisal University, Al-Ahsaa 31982, Saudi Arabia
4Theoretical Physics Group, Faculty of Sciences, Chouaib Doukkali University, El Jadida 24000, Morocco

Received 20 March 2012; Accepted 30 May 2012

Academic Editor: Sanith Wijesinghe

Copyright © 2012 A. D. Alhaidari et al. 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.


We obtain exact scattering solutions of the Dirac equation in 1 + 1 dimensions for a double square barrier vector potential. The potential bottom between the two barriers is chosen to be higher than 2mc2, whereas the top of the barriers is at least 2mc2 above the bottom. The relativistic version of the conventional double barrier transmission resonances is obtained for energies within ±mc2 from the height of the barriers. However, due to our judicious choice of potential configuration we also find two more (subbarrier) transmission resonance regions below the conventional one. Both are located within the two Klein energy zones and characterized by resonances that are broader than the conventional ones. The design of our double barrier so as to enable us to establish these two new subbarrier transmission resonance regions is our main finding.