Solution of one-dimensional Dirac equation via Poincaré map

Solution of one-dimensional Dirac equation via Poincaré map

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 rap...

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Veröffentlicht in:Europhysics letters 2011-07, Vol.95 (1), p.17009
Hauptverfasser: Bahlouli, Hocine, Choubabi, El Bouâzzaoui, Jellal, Ahmed
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container_title Europhysics letters
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creator Bahlouli, Hocine
Choubabi, El Bouâzzaoui
Jellal, Ahmed
description 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.
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title Solution of one-dimensional Dirac equation via Poincaré map
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