标题： 一维狄拉克方程的庞加莱映射解法 显示英文标题

标题： Solution of One-dimensional Dirac Equation via Poincare Map

摘要： 我们使用“庞加莱映射”方法求解一般的二维狄拉克方程，该方法避免了对空间导数的任何近似，并将问题简化为一个简单的递归关系，从数值实现的角度来看非常实用。 为了测试该方法的效率和快速收敛性，我们将它应用于一个矢量耦合伍兹-萨森势，该势是精确可解的。 与现有的解析结果进行比较令人印象深刻，从而验证了该方法的准确性和效率。 显示英文摘要

摘要： 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.