Volume 95, Number 1, July 2011
|Number of page(s)||5|
|Section||Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties|
|Published online||21 June 2011|
Solution of one-dimensional Dirac equation via Poincaré map
Saudi Center for Theoretical Physics - Dhahran, Saudi Arabia
2 Physics Department, King Fahd University of Petroleum & Minerals - Dhahran 31261, Saudi Arabia
3 Theoretical Physics Group, Faculty of Sciences, Chouaïb Doukkali University - PO Box 20, 24000 El Jadida, Morocco
4 Physics Department, College of Sciences, King Faisal University - PO Box 380, Alahsa 31982, Saudi Arabia
Accepted: 20 May 2011
We solve the general one-dimensional Dirac equation using a “Poincaré map” approach which avoids any approximation to the spacial derivatives and reduces the problem to a simple recursive relation which is very practical from the numerical implementation point of view. To test the efficiency and rapid convergence of this approach we apply it to a vector coupling Woods-Saxon potential, which is exactly solvable. Comparison with available analytical results is impressive and hence validates the accuracy and efficiency of this method.
PACS: 73.63.-b – Electronic transport in nanoscale materials and structures / 73.23.-b – Electronic transport in mesoscopic systems / 11.80.-m – Relativistic scattering theory
© EPLA, 2011
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