Solution of One-dimensional Dirac Equation via Poincare Map

Details Solution of One-dimensional Dirac Equation via Poincare Map Solution of One-dimensional Dirac Equation via Poincare Map

2011-05-24

arxiv.org/abs/1105.4741v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, 6 figures. Version to appear in EPL

Scientific paper

We solve the general one-dimensional Dirac equation using a "Poincare 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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