Solution of One-dimensional Dirac Equation via Poincare Map
arXiv:1105.4741 · doi:10.1209/0295-5075/95/17009
Abstract
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.
8 pages, 6 figures. Version to appear in EPL