Solution of One-dimensional Dirac Equation via Poincare Map
  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. 
Hocine Bahlouli, El Bouazzaoui Choubabi, Ahmed Jellal
hep-th cond-mat.mes-hall math-ph math.MP quant-ph